##DESCRIPTION
## DBsubject('')
## DBchapter('')
## DBsection('')
## KEYWORDS('', '')
## Author('')
## Institution('')
##ENDDESCRIPTION


DOCUMENT();      

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl", 
"PGgraphmacros.pl",
"PGasu.pl",
"unionTables.pl","unionMacros.pl"
);
#######################
TEXT($BEGIN_ONE_COLUMN,beginproblem()) ;
$refreshCachedImages = 1;
$showPartialCorrectAnswers = 1;
###############
#  case 0 - LL90 pythagoras 
#  case 0.1 - LL90 pythagoras - small sides
#  case 0.2 - LL90 pythagoras - large sides
#  case 0.3 - LL90 pythagoras - scientific notation
#  case 1 - HL90 pythagoras
#  case 1.1 - HL90 pythagoras - small sides
#  case 1.2 - HL90 pythagoras - large sides
#  case 1.3 - HL90 pythagoras - scientific notation
#  case 2 - LL90 solve
#  case 2.1 - LL90 solve - small numbers
#  case 2.2 - LL90 solve - large numbers
#  case 2.3 - LL90 solve - scientific notation
#  case 3 - HL90 solve
#  case 3.1 - HL90 solve - small numbers
#  case 3.2 - HL90 solve - large numbers
#  case 3.3 - HL90 solve - scientific notation
#  case 4 - AL90 solve
#  case 4.1 - AL90 solve - small numbers
#  case 4.2 - AL90 solve - large numbers
#  case 4.3 - AL90 solve - scientific notation
#  case 5 - AH90 solve
#  case 5.1 - AH90 solve - small numbers
#  case 5.2 - AH90 solve - large numbers
#  case 5.3 - AH90 solve - scientific notation
#  case 6 - sss   - random largest angle
#  case 6.1 - sss   - random largest angle - small numbers
#  case 6.2 - sss   - random largest angle - large numbers
#  case 6.3 - sss   - random largest angle - scientific notation
#  case 6.4 - sss   - one angle obtuse
#  case 6.5 - sss   - one angle obtuse - small numbers
#  case 6.6 - sss   - one angle obtuse - large numbers
#  case 6.7 - sss   - one anngle obtuse - scientific notation
#  case 7 - sas  cosine law acute
#  case 7.1 - sas  cosine law acute small sides
#  case 7.2 - sas  cosine law acute  large sides
#  case 7.3 - sas  cosine law acute   scientific notation
#  case 8 - sas  cosine law obtuse
#  case 8.1 - sas  cosine law obtuse small sides
#  case 8.2 - sas  cosine law obtuse  large sides
#  case 8.3 - sas  cosine law obtuse   scientific notation
#  case 9 - ass   acute
#  case 9.1 - ass   acute  - small sides
#  case 9.2 - ass   acute  - large sides
#  case 9.3 - ass   acute  - scientific notation
#  case 10 - ass   obtuse 
#  case 10.1 - ass obtuse - small sides
#  case 10.2 - ass  obtuse - large sides
#  case 10.3 - ass obtuse - scientific notation
#  case 11 - asa
#  case 11.1 - asa - small sides
#  case 11.2 - asa - large sides
#  case 11.3 - asa - scientific notation
###########################################

@case = (0,1,2,3,4,5);
@case = @case [NchooseK(6,6)];
@case = (0,0.1,0.2,0.3,1,1.1,1.2,1.3,2,2.1,2.2,2.3,3,3.1,3.2,3.3,4,4.1,4.2,4.3,5,5.1,5.2,5.3,6,6.1,6.2,6.3,6.4,6.5,6.6,6.7,7,7.1,7.2,7.3,8,8.1,8.2,8.3,9,9.1,9.2,9.3,10,10.1,10.2,10.3,11,11.1,11.2,11.3);






$trial = 0;


$deg = "".sprintf("%c",0xb0);


@n3k = NchooseK(3,3);

	foreach my $case (@case) {
		# do something for each frame
	$trial = $trial + 1;
        $TABLEoverride = 0;
if( scalar (@list) <2){@list = (5,6,7,8,9,10,11,12,13,14,15);
@list = @list [NchooseK(11,11)];
@list = (@list,@list[0,2,4,6,8,10,1,3,5,7,9])
}       

if( scalar (@listsd) <1){@listsd = (4,5,6,7,8,9);
@listsd = @listsd [NchooseK(6,6)];
@listdd = (11,12,13,14,15,16);
@listdd = @listdd [NchooseK(6,6)];

@listsd = (@listsd, @listsd,@listsd);
@listdd = (@listdd,@listdd[1,2,3,4,5,0], @listdd[2,3,4,5,0,1])
}  
if( scalar (@AcuteList) <2){@AcuteList = (20,30,40,55,65,75);
@AcuteList = @AcuteList [NchooseK(6,6)];
@AcuteList = (@AcuteList,@AcuteList[0,1,3,5,2,4])}


if( scalar (@SmallAcuteList) <2){@SmallAcuteList = (10,15,20,25,30,35);
@SmallAcuteList = @SmallAcuteList [NchooseK(6,6)];
@SmallAcuteList = (@SmallAcuteList,@SmallAcuteList[0,1,3,5,2,4])}



if( scalar (@ObtuseList) <2){@ObtuseList = (110,130,140,155 ,115,135);
@ObtuseList = @ObtuseList [NchooseK(6,6)];
@ObtuseList = (@ObtuseList,@ObtuseList[0,1,3,5,2,4])}

@listSingleDigit = (4,5,6,7,8,9);
@listDoubleDigit = (11,12,13,14,15,16);


@n3k = @n3k[1,2,0];
if($trial/3 == int($trial/3)){@n3k = @n3k[0,2,1]}

# Sets of labels vvvvvvvvvvvvvvvvvvvv
@Angles = ("A","B","C","W","X","Y","X","Y","Z","I","J","K");
@Sides = ("a","b","c","w","x","y","x","y","z","i","j","k");
$tmpSTART = random(0,9,3);
$AL = @Angles[$tmpSTART + 0];
$LL[$n3k[0]] = $AL;
$BL = @Angles[$tmpSTART + 1];
$LL[$n3k[1]] = $BL;
$CL = @Angles[$tmpSTART + 2];
$LL[$n3k[2]] = $CL;
$aL = @Sides[$tmpSTART + 0];
$ll[$n3k[0]] = $aL;
$bL = @Sides[$tmpSTART + 1];
$ll[$n3k[1]] = $bL;
$cL = @Sides[$tmpSTART + 2];
$ll[$n3k[2]] = $cL;
# Sets of labels ^^^^^^^^^^^^^^^^^^^


if ($case == 0){   ###LL90 find hyptoneuse only






$x[1] = pop @list;
$X[0] = 90;

$x[2] = pop @list;




$x[0] = sqrt($x[1]**2 + $x[2]**2 ); #the hypotenuse
$X[1] = 180 / $PI * asin( $x[1] / $x[0] );
$X[2] = 180 - $X[0] - $X[1];


$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "";
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "= ". $x[2];
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];



##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
      $table = BeginTable(spacing => 3);

$TABLEoverride = 1;
        $table .= AlignedRow(["The length of side $ll[0] is ",NAMED_ANS_RULE("answer".$trial,6)]);


push @namedCmp , "answer".$trial=>num_cmp( $x[0], reltol=>3  ) ;  
      
      


        $table .= EndTable();
}
if ($case == 0.1){   ###LL90 find hyptoneuse only small numbers
$fact =0.001;


$x[1] = pop @list;
$X[0] = 90;
$x[2] =  pop @list; # the other leg

$x[0] = sqrt($x[1]**2 + $x[2]**2 ); #the hypotenuse
$X[1] = 180 / $PI * asin( $x[1] / $x[0] );
$X[2] = 180 - $X[0] - $X[1];
for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact}  

$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "";
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "= ". $x[2];
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];



##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
      $table = BeginTable(spacing => 3);


        $table .= AlignedRow(["The length of side $ll[0] is ",NAMED_ANS_RULE("answer".$trial,6)]);


push @namedCmp , "answer".$trial=>num_cmp( $x[0], reltol=>3  ) ;  
      
      


        $table .= EndTable();
}

if ($case == 0.2){   ###LL90 find hyptoneuse only, large numbers

$fact =list_random(100,1000);


$x[1] = pop @list;
$X[0] = 90;
$x[2] =  pop @list; # the other leg

$x[0] = sqrt($x[1]**2 + $x[2]**2 ); #the hypotenuse
$X[1] = 180 / $PI * asin( $x[1] / $x[0] );
$X[2] = 180 - $X[0] - $X[1];
for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 



$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "";
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "= ". $x[2];
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];



##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
      $table = BeginTable(spacing => 3);

        $table .= AlignedRow(["The length of side $ll[0] is ",NAMED_ANS_RULE("answer".$trial,6)]);


push @namedCmp , "answer".$trial=>num_cmp( $x[0], reltol=>3  ) ;  
      
      


        $table .= EndTable();
}



if ($case == 0.3){   ###LL90 find hyptoneuse only, large numbers

$fact = list_random(10**(-20), 10**(-15), 10**30, 10**40);



$x[1] =  pop  @listsd;
$X[0] = 90;
$x[2] =  pop @listdd; # the other leg




$x[0] = sqrt($x[1]**2 + $x[2]**2 ); #the hypotenuse
$X[1] = 180 / $PI * asin( $x[1] / $x[0] );
$X[2] = 180 - $X[0] - $X[1];


for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 

$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "";
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "= ". $x[2];
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];



##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
      $table = BeginTable(spacing => 3);


        $table .= AlignedRow(["The length of side $ll[0] is ",NAMED_ANS_RULE("answer".$trial,6)]);


push @namedCmp , "answer".$trial=>num_cmp( $x[0], reltol=>3  ) ;  
      
      


        $table .= EndTable();
}


if ($case == 1){   ###HL90 missing side only



$x[1] = pop @list;
$X[0] = 90;

$x[0] = random(int(1.2 * $x[1] + 1),int(5 * $x[1])); # the hypotenuse



$X[1] = 180 / $PI * asin( $x[1] / $x[0] );
$X[2] = 180 - $X[0] - $X[1];
$x[2] = sqrt($x[0]**2 - $x[1]**2 );




$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "= ". $x[0];
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];



##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
      $table = BeginTable(spacing => 3);


        $table .= AlignedRow(["The length of side $ll[2] is ",NAMED_ANS_RULE("answer".$trial,6)]);


push @namedCmp , "answer".$trial=>num_cmp( $x[2], reltol=>3  ) ;  
      
      


        $table .= EndTable();
}



if ($case == 1.1){   ###HL90 missing side only - small values

$fact = list_random(0.01,0.001,0.0001);

$x[1] = pop @list;
$X[0] = 90;

$x[0] = random(int(1.2 * $x[1] + 1),int(5 * $x[1])); # the hypotenuse



$X[1] = 180 / $PI * asin( $x[1] / $x[0] );
$X[2] = 180 - $X[0] - $X[1];
$x[2] = sqrt($x[0]**2 - $x[1]**2 );

for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 


$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "= ". $x[0];
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];



##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
      $table = BeginTable(spacing => 3);

        $table .= AlignedRow(["The length of side $ll[2] is ",NAMED_ANS_RULE("answer".$trial,6)]);


push @namedCmp , "answer".$trial=>num_cmp( $x[2], reltol=>3  ) ;  
      
      


        $table .= EndTable();
}
if ($case == 1.2){   ###HL90 missing side only  large values




$fact = list_random(100,1000,10000);

$x[1] = pop @list;
$X[0] = 90;

$x[0] = random(int(1.2 * $x[1] + 1),int(5 * $x[1])); # the hypotenuse



$X[1] = 180 / $PI * asin( $x[1] / $x[0] );
$X[2] = 180 - $X[0] - $X[1];
$x[2] = sqrt($x[0]**2 - $x[1]**2 );

for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 
$x[2] = sqrt($x[0]**2 - $x[1]**2 );


for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 


$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "= ". $x[0];
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];



##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
      $table = BeginTable(spacing => 3);


        $table .= AlignedRow(["The length of side $ll[2] is ",NAMED_ANS_RULE("answer".$trial,6)]);


push @namedCmp , "answer".$trial=>num_cmp( $x[2], reltol=>3  ) ;  
      
      


        $table .= EndTable();
}


if ($case == 1.3){   ###HL90 missing side only

$fact = list_random(10**(-40), 10**(-16), 10**29, 10**41);

$x[1] = pop @list;
$X[0] = 90;

$x[0] = random(int(1.2 * $x[1] + 1),int(5 * $x[1])); # the hypotenuse



$X[1] = 180 / $PI * asin( $x[1] / $x[0] );
$X[2] = 180 - $X[0] - $X[1];
$x[2] = sqrt($x[0]**2 - $x[1]**2 );

for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 
$x[2] = sqrt($x[0]**2 - $x[1]**2 );


for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 

$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "= ". $x[0];
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];



##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
      $table = BeginTable(spacing => 3);


        $table .= AlignedRow(["The length of side $ll[2] is ",NAMED_ANS_RULE("answer".$trial,6)]);


push @namedCmp , "answer".$trial=>num_cmp( $x[2], reltol=>3  ) ;  
      
      


        $table .= EndTable();
}







if ($case == 2){   ###LL90 solve

$fact = 1;

$x[1] = pop @list;
$X[0] = 90;
$x[2] =  pop @list; # the other leg




$x[0] = sqrt($x[1]**2 + $x[2]**2 ); #the hypotenuse
$X[1] = 180 / $PI * asin( $x[1] / $x[0] );
$X[2] = 180 - $X[0] - $X[1];

for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 

$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "";
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "= ". $x[2];
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];

##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv

$table = BeginTable(spacing => 3);


        $table .= AlignedRow([" $ll[0] = ",NAMED_ANS_RULE("hyp".$trial,6)]);

        push @namedCmp , "hyp".$trial=>num_cmp( $x[0], reltol=>3  ) ; 
 
  $table .= AlignedRow(["\( \angle $LL[1] = \)",NAMED_ANS_RULE("angle1".$trial,6),]);
push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ;  

  $table .= AlignedRow(["\( \angle $LL[2] = \)",NAMED_ANS_RULE("angle2".$trial,6),]);
push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ;  

        $table .= EndTable();

}

if ($case == 2.1){   ###LL90 solve  small sides


$fact = list_random(0.01,0.001,0.0001);

$x[1] = pop @list;
$X[0] = 90;
$x[2] =  pop @list; # the other leg




$x[0] = sqrt($x[1]**2 + $x[2]**2 ); #the hypotenuse
$X[1] = 180 / $PI * asin( $x[1] / $x[0] );
$X[2] = 180 - $X[0] - $X[1];

for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 



$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "";
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "= ". $x[2];
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];

##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
 
$table = BeginTable(spacing => 3);


        $table .= AlignedRow([" $ll[0] = ",NAMED_ANS_RULE("hyp".$trial,6)]);

        push @namedCmp , "hyp".$trial=>num_cmp( $x[0], reltol=>3  ) ; 
 
  $table .= AlignedRow(["\( \angle $LL[1] = \)",NAMED_ANS_RULE("angle1".$trial,6),]);
push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ;  

  $table .= AlignedRow(["\( \angle $LL[2] = \)",NAMED_ANS_RULE("angle2".$trial,6),]);
push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ;  

        $table .= EndTable();

}

if ($case == 2.2){   ###LL90 solve



$fact = list_random(0.01,0.001,0.0001);

$x[1] = pop @list;
$X[0] = 90;
$x[2] =  pop @list; # the other leg




$x[0] = sqrt($x[1]**2 + $x[2]**2 ); #the hypotenuse
$X[1] = 180 / $PI * asin( $x[1] / $x[0] );
$X[2] = 180 - $X[0] - $X[1];

for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 



$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "";
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "= ". $x[2];
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];

##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
 
$table = BeginTable(spacing => 3);


        $table .= AlignedRow([" $ll[0] = ",NAMED_ANS_RULE("hyp".$trial,6)]);

        push @namedCmp , "hyp".$trial=>num_cmp( $x[0], reltol=>3  ) ; 
 
  $table .= AlignedRow(["\( \angle $LL[1] = \)",NAMED_ANS_RULE("angle1".$trial,6),]);
push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ;  

  $table .= AlignedRow(["\( \angle $LL[2] = \)",NAMED_ANS_RULE("angle2".$trial,6),]);
push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ;  

        $table .= EndTable();

}

if ($case == 2.3){   ###LL90 solve scientific notation





$fact = list_random(10**40,10**41,10**-20,10**-21);

$x[1] = pop @listsd;
$X[0] = 90;
$x[2] =  pop @listdd; # the other leg




$x[0] = sqrt($x[1]**2 + $x[2]**2 ); #the hypotenuse
$X[1] = 180 / $PI * asin( $x[1] / $x[0] );
$X[2] = 180 - $X[0] - $X[1];

for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 




$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "";
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "= ". $x[2];
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];

##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
   
$table = BeginTable(spacing => 3);


        $table .= AlignedRow([" $ll[0] = ",NAMED_ANS_RULE("hyp".$trial,6)]);

        push @namedCmp , "hyp".$trial=>num_cmp( $x[0], reltol=>3  ) ; 
 
  $table .= AlignedRow(["\( \angle $LL[1] = \)",NAMED_ANS_RULE("angle1".$trial,6),]);
push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ;  

  $table .= AlignedRow(["\( \angle $LL[2] = \)",NAMED_ANS_RULE("angle2".$trial,6),]);
push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ;  

        $table .= EndTable();

}







if ($case == 3){   ###HL90 solve

$fact = 1;

$x[1] = pop @list;
$X[0] = 90;

$x[0] = random(int(1.2 * $x[1] + 1),int(5 * $x[1])); # the hypotenuse



$X[1] = 180 / $PI * asin( $x[1] / $x[0] );
$X[2] = 180 - $X[0] - $X[1];
$x[2] = sqrt($x[0]**2 - $x[1]**2 );


for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 


$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "= ". $x[0];
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";

$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];


##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
 
$table = BeginTable(spacing => 3);


        $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("hyp".$trial,6)]);

        push @namedCmp , "hyp".$trial=>num_cmp( $x[0], reltol=>3  ) ; 
 
  $table .= AlignedRow(["\( \angle $LL[1] = \)",NAMED_ANS_RULE("angle1".$trial,6),]);
push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ;  

  $table .= AlignedRow(["\( \angle $LL[2] = \)",NAMED_ANS_RULE("angle2".$trial,6),]);
push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ;  

        $table .= EndTable();

}

if ($case == 3.1){   ###HL90 solve


$fact = list_random(0.001,0.0001,0.01);

$x[1] = pop @list;
$X[0] = 90;

$x[0] = random(int(1.2 * $x[1] + 1),int(5 * $x[1])); # the hypotenuse



$X[1] = 180 / $PI * asin( $x[1] / $x[0] );
$X[2] = 180 - $X[0] - $X[1];
$x[2] = sqrt($x[0]**2 - $x[1]**2 );


for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 




$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "= ". $x[0];
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";

$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];


##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
  
$table = BeginTable(spacing => 3);


        $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("hyp".$trial,6)]);

        push @namedCmp , "hyp".$trial=>num_cmp( $x[0], reltol=>3  ) ; 
 
  $table .= AlignedRow(["\( \angle $LL[1] = \)",NAMED_ANS_RULE("angle1".$trial,6),]);
push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ;  

  $table .= AlignedRow(["\( \angle $LL[2] = \)",NAMED_ANS_RULE("angle2".$trial,6),]);
push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ;  

        $table .= EndTable();

}

if ($case == 3.2){   ###HL90 solve  large angles



$fact = list_random(100,1000,10000);

$x[1] = pop @list;
$X[0] = 90;

$x[0] = random(int(1.2 * $x[1] + 1),int(5 * $x[1])); # the hypotenuse



$X[1] = 180 / $PI * asin( $x[1] / $x[0] );
$X[2] = 180 - $X[0] - $X[1];
$x[2] = sqrt($x[0]**2 - $x[1]**2 );


for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 




$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "= ". $x[0];
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";

$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];


##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
 
$table = BeginTable(spacing => 3);


        $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("hyp".$trial,6)]);

        push @namedCmp , "hyp".$trial=>num_cmp( $x[0], reltol=>3  ) ; 
 
  $table .= AlignedRow(["\( \angle $LL[1] = \)",NAMED_ANS_RULE("angle1".$trial,6),]);
push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ;  

  $table .= AlignedRow(["\( \angle $LL[2] = \)",NAMED_ANS_RULE("angle2".$trial,6),]);
push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ;  

        $table .= EndTable();

}


if ($case == 3.3){   ###HL90 solve  scientific notation
$fact = list_random(10**-30,10**-31,10**20,10**21);

$x[1] = pop @listsd;
$X[0] = 90;

$x[0] = pop @listdd; # the hypotenuse



$X[1] = 180 / $PI * asin( $x[1] / $x[0] );
$X[2] = 180 - $X[0] - $X[1];
$x[2] = sqrt($x[0]**2 - $x[1]**2 );


for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 




$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "= ". $x[0];
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";

$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];


##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
 
$table = BeginTable(spacing => 3);


        $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("hyp".$trial,6)]);

        push @namedCmp , "hyp".$trial=>num_cmp( $x[0], reltol=>3  ) ; 
 
  $table .= AlignedRow(["\( \angle $LL[1] = \)",NAMED_ANS_RULE("angle1".$trial,6),]);
push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ;  

  $table .= AlignedRow(["\( \angle $LL[2] = \)",NAMED_ANS_RULE("angle2".$trial,6),]);
push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ;  

        $table .= EndTable();

}


if ($case == 4){   ###as90 

$fact = 1;
# given vvvvvvvvvvvvvvv
$x[1] = pop @list;
$X[0] = pop @AcuteList;

$X[2] = 90;
# given ^^^^^^^^^^^^^^^^^^^^^^


$X[1] = 180 - $X[0] - $X[2] ;
$x[2] =  $x[1]  / sin ($PI / 180 * $X[1]);
$x[0] = sin ($PI / 180 * $X[0]) * $x[1]  / sin ($PI / 180 * $X[1]);


for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 


$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "=".$X[2].$deg;
$a = $x[$n3k[0]];
$given[0] = "";
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];



##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
  
$table = BeginTable(spacing => 3);
        $table .= AlignedRow([" $ll[0] = ",NAMED_ANS_RULE("leg".$trial,6)]);

        push @namedCmp , "leg".$trial=>num_cmp( $x[0], reltol=>3  ) ; 

        $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("hyp".$trial,6)]);

        push @namedCmp , "hyp".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 
  $table .= AlignedRow(["\( \angle $LL[1] = \)",NAMED_ANS_RULE("angle1".$trial,6),]);
push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ;  

 

        $table .= EndTable();
}

if ($case == 4.1){   ###as90 small numbers


$fact = list_random(0.01,0.001,0.001);
# given vvvvvvvvvvvvvvv
$x[1] = pop @list;
$X[0] = pop @AcuteList;

$X[2] = 90;
# given ^^^^^^^^^^^^^^^^^^^^^^


$X[1] = 180 - $X[0] - $X[2] ;
$x[2] =  $x[1]  / sin ($PI / 180 * $X[1]);
$x[0] = sin ($PI / 180 * $X[0]) * $x[1]  / sin ($PI / 180 * $X[1]);


for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 





$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "=".$X[2].$deg;
$a = $x[$n3k[0]];
$given[0] = "";
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];



##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
  
$table = BeginTable(spacing => 3);
        $table .= AlignedRow([" $ll[0] = ",NAMED_ANS_RULE("leg".$trial,6)]);

        push @namedCmp , "leg".$trial=>num_cmp( $x[0], reltol=>3  ) ; 

        $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("hyp".$trial,6)]);

        push @namedCmp , "hyp".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 
  $table .= AlignedRow(["\( \angle $LL[1] = \)",NAMED_ANS_RULE("angle1".$trial,6),]);
push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ;  

 

        $table .= EndTable();
}
if ($case == 4.2){   ###as90  large numbers


$fact = list_random(1000,10000,100);
# given vvvvvvvvvvvvvvv
$x[1] = pop @list;
$X[0] = pop @AcuteList;

$X[2] = 90;
# given ^^^^^^^^^^^^^^^^^^^^^^


$X[1] = 180 - $X[0] - $X[2] ;
$x[2] =  $x[1]  / sin ($PI / 180 * $X[1]);
$x[0] = sin ($PI / 180 * $X[0]) * $x[1]  / sin ($PI / 180 * $X[1]);


for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 





$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "=".$X[2].$deg;
$a = $x[$n3k[0]];
$given[0] = "";
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];



##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
 
$table = BeginTable(spacing => 3);
        $table .= AlignedRow([" $ll[0] = ",NAMED_ANS_RULE("leg".$trial,6)]);

        push @namedCmp , "leg".$trial=>num_cmp( $x[0], reltol=>3  ) ; 

        $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("hyp".$trial,6)]);

        push @namedCmp , "hyp".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 
  $table .= AlignedRow(["\( \angle $LL[1] = \)",NAMED_ANS_RULE("angle1".$trial,6),]);
push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ;  

 

        $table .= EndTable();
}



if ($case == 4.3){   ###as90  scientific notation


$fact = list_random(10**100,10**43,10**-39,10**-20);
# given vvvvvvvvvvvvvvv
$x[1] = pop @list;
$X[0] = pop @AcuteList;

$X[2] = 90;
# given ^^^^^^^^^^^^^^^^^^^^^^


$X[1] = 180 - $X[0] - $X[2] ;
$x[2] =  $x[1]  / sin ($PI / 180 * $X[1]);
$x[0] = sin ($PI / 180 * $X[0]) * $x[1]  / sin ($PI / 180 * $X[1]);


for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 





$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "=".$X[2].$deg;
$a = $x[$n3k[0]];
$given[0] = "";
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];



##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv

$table = BeginTable(spacing => 3);
        $table .= AlignedRow([" $ll[0] = ",NAMED_ANS_RULE("leg".$trial,6)]);

        push @namedCmp , "leg".$trial=>num_cmp( $x[0], reltol=>3  ) ; 

        $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("hyp".$trial,6)]);

        push @namedCmp , "hyp".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 
  $table .= AlignedRow(["\( \angle $LL[1] = \)",NAMED_ANS_RULE("angle1".$trial,6),]);
push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ;  

 

        $table .= EndTable();
}




if ($case == 5){   ###ah90 

$fact = 1;
# given vvvvvvvvvvvvvvv
$x[1] = pop @list;
$X[0] = pop @AcuteList;

$X[1] = 90;
# given ^^^^^^^^^^^^^^^^^^^^^^


$X[2] = 180 - $X[0] - $X[1] ;
$x[2] = sin ($PI / 180 * $X[2]) * $x[1]  ;
$x[0] = sin ($PI / 180 * $X[0]) * $x[1] ;

for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 




$A = $X[$n3k[0]];
$Given[0] = " = ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = " = ".$X[1].$deg;
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "";
$b = $x[$n3k[1]];
$given[1] = " = ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];





##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
 
$table = BeginTable(spacing => 3);
        $table .= AlignedRow([" $ll[0] = ",NAMED_ANS_RULE("leg".$trial,6)]);

        push @namedCmp , "leg".$trial=>num_cmp( $x[0], reltol=>3  ) ; 

        $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("hyp".$trial,6)]);

        push @namedCmp , "hyp".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 
  $table .= AlignedRow(["\( \angle $LL[2] = \)",NAMED_ANS_RULE("angle2".$trial,6),]);
push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ;  

 

        $table .= EndTable();
}

if ($case == 5.1){   ###ah90 small numbers 


$fact = list_random(0.001,0.001,0.1);
# given vvvvvvvvvvvvvvv
$x[1] = pop @list;
$X[0] = pop @AcuteList;

$X[1] = 90;
# given ^^^^^^^^^^^^^^^^^^^^^^


$X[2] = 180 - $X[0] - $X[1] ;
$x[2] = sin ($PI / 180 * $X[2]) * $x[1]  ;
$x[0] = sin ($PI / 180 * $X[0]) * $x[1] ;

for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 






$A = $X[$n3k[0]];
$Given[0] = " = ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = " = ".$X[1].$deg;
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "";
$b = $x[$n3k[1]];
$given[1] = " = ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];





##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
 
$table = BeginTable(spacing => 3);
        $table .= AlignedRow([" $ll[0] = ",NAMED_ANS_RULE("leg".$trial,6)]);

        push @namedCmp , "leg".$trial=>num_cmp( $x[0], reltol=>3  ) ; 

        $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("hyp".$trial,6)]);

        push @namedCmp , "hyp".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 
  $table .= AlignedRow(["\( \angle $LL[2] = \)",NAMED_ANS_RULE("angle2".$trial,6),]);
push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ;  

 

        $table .= EndTable();
}


if ($case == 5.2){   ###ah90 -large numbers



$fact = list_random(100,1000,10000);
# given vvvvvvvvvvvvvvv
$x[1] = pop @list;
$X[0] = pop @AcuteList;

$X[1] = 90;
# given ^^^^^^^^^^^^^^^^^^^^^^


$X[2] = 180 - $X[0] - $X[1] ;
$x[2] = sin ($PI / 180 * $X[2]) * $x[1]  ;
$x[0] = sin ($PI / 180 * $X[0]) * $x[1] ;

for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 







$A = $X[$n3k[0]];
$Given[0] = " = ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = " = ".$X[1].$deg;
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "";
$b = $x[$n3k[1]];
$given[1] = " = ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];





##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
   
$table = BeginTable(spacing => 3);
        $table .= AlignedRow([" $ll[0] = ",NAMED_ANS_RULE("leg".$trial,6)]);

        push @namedCmp , "leg".$trial=>num_cmp( $x[0], reltol=>3  ) ; 

        $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("hyp".$trial,6)]);

        push @namedCmp , "hyp".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 
  $table .= AlignedRow(["\( \angle $LL[2] = \)",NAMED_ANS_RULE("angle2".$trial,6),]);
push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ;  

 

        $table .= EndTable();
}



if ($case == 5.3){   ###ah90 -scientific notation



$fact = list_random(10**45, 10**43,10**-20,10**-19);
# given vvvvvvvvvvvvvvv
$x[1] = pop @list;
$X[0] = pop @AcuteList;

$X[1] = 90;
# given ^^^^^^^^^^^^^^^^^^^^^^


$X[2] = 180 - $X[0] - $X[1] ;
$x[2] = sin ($PI / 180 * $X[2]) * $x[1]  ;
$x[0] = sin ($PI / 180 * $X[0]) * $x[1] ;

for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 







$A = $X[$n3k[0]];
$Given[0] = " = ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = " = ".$X[1].$deg;
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "";
$b = $x[$n3k[1]];
$given[1] = " = ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];





##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
   
$table = BeginTable(spacing => 3);
        $table .= AlignedRow([" $ll[0] = ",NAMED_ANS_RULE("leg".$trial,6)]);

        push @namedCmp , "leg".$trial=>num_cmp( $x[0], reltol=>3  ) ; 

        $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("hyp".$trial,6)]);

        push @namedCmp , "hyp".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 
  $table .= AlignedRow(["\( \angle $LL[2] = \)",NAMED_ANS_RULE("angle2".$trial,6),]);
push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ;  

 

        $table .= EndTable();
}


if ($case == 6){   ###sss   random largest angle 

$fact = 1;
@printtest = @list;
$x[0] = pop @list;
$x[1] = pop @list;
$x[2] = random( abs($x[0] - $x[1])+2, $x[0] + $x[1] - 2 );


#use cosine law to find angles
$X[0] = (180/$PI)*acos ((  $x[1]**2 + $x[2]**2- $x[0]**2)/(2*$x[1]*$x[2])); 
$X[1] = (180/$PI)*acos ((  $x[0]**2 + $x[2]**2- $x[1]**2)/(2*$x[0]*$x[2]));

$X[2] = 180 - $X[0] - $X[1] ;
for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 


$A = $X[$n3k[0]];
$Given[0] = "";
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] =" = ". $x[0];
$b = $x[$n3k[1]];
$given[1] = " = ". $x[1];
$c = $x[$n3k[2]];
$given[2] = " = ". $x[2];
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];





##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
  
$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[0] = ",NAMED_ANS_RULE("angle0".$trial,6)]);
        push @namedCmp , "angle0".$trial=>num_cmp( $X[0], reltol=>3  ) ; 

         $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $LL[2] = ",NAMED_ANS_RULE("angle2".$trial,6)]);
        push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ; 
 

        $table .= EndTable();
}




if ($case == 6.1){   ###sss   random largest angle - small numbers


$fact = list_random(0.01,0.001,0.0001);
@printtest = @list;
$x[0] = pop @list;
$x[1] = pop @list;
$x[2] = random( abs($x[0] - $x[1])+2, $x[0] + $x[1] - 2 );


#use cosine law to find angles
$X[0] = (180/$PI)*acos ((  $x[1]**2 + $x[2]**2- $x[0]**2)/(2*$x[1]*$x[2])); 
$X[1] = (180/$PI)*acos ((  $x[0]**2 + $x[2]**2- $x[1]**2)/(2*$x[0]*$x[2]));

$X[2] = 180 - $X[0] - $X[1] ;
for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 


$A = $X[$n3k[0]];
$Given[0] = "";
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] =" = ". $x[0];
$b = $x[$n3k[1]];
$given[1] = " = ". $x[1];
$c = $x[$n3k[2]];
$given[2] = " = ". $x[2];
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];


##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
 
$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[0] = ",NAMED_ANS_RULE("angle0".$trial,6)]);
        push @namedCmp , "angle0".$trial=>num_cmp( $X[0], reltol=>3  ) ; 

         $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $LL[2] = ",NAMED_ANS_RULE("angle2".$trial,6)]);
        push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ; 
 

        $table .= EndTable();
}

if ($case == 6.2){   ###sss   random largest angle - large numbers


$fact = list_random(100,10000,1000);
@printtest = @list;
$x[0] = pop @list;
$x[1] = pop @list;
$x[2] = random( abs($x[0] - $x[1])+2, $x[0] + $x[1] - 2 );


#use cosine law to find angles
$X[0] = (180/$PI)*acos ((  $x[1]**2 + $x[2]**2- $x[0]**2)/(2*$x[1]*$x[2])); 
$X[1] = (180/$PI)*acos ((  $x[0]**2 + $x[2]**2- $x[1]**2)/(2*$x[0]*$x[2]));

$X[2] = 180 - $X[0] - $X[1] ;
for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 


$A = $X[$n3k[0]];
$Given[0] = "";
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] =" = ". $x[0];
$b = $x[$n3k[1]];
$given[1] = " = ". $x[1];
$c = $x[$n3k[2]];
$given[2] = " = ". $x[2];
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];





##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
 
$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[0] = ",NAMED_ANS_RULE("angle0".$trial,6)]);
        push @namedCmp , "angle0".$trial=>num_cmp( $X[0], reltol=>3  ) ; 

         $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $LL[2] = ",NAMED_ANS_RULE("angle2".$trial,6)]);
        push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ; 
 

        $table .= EndTable();}



if ($case == 6.3){   ###sss   random largest angle - scientific notation


$fact = list_random(10**40,10**41,10**-40,10**-41);
@printtest = @list;
$x[0] = pop @list;
$x[1] = pop @list;
$x[2] = random( abs($x[0] - $x[1])+2, $x[0] + $x[1] - 2 );


#use cosine law to find angles
$X[0] = (180/$PI)*acos ((  $x[1]**2 + $x[2]**2- $x[0]**2)/(2*$x[1]*$x[2])); 
$X[1] = (180/$PI)*acos ((  $x[0]**2 + $x[2]**2- $x[1]**2)/(2*$x[0]*$x[2]));

$X[2] = 180 - $X[0] - $X[1] ;
+


$A = $X[$n3k[0]];
$Given[0] = "";
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] =" = ". $x[0];
$b = $x[$n3k[1]];
$given[1] = " = ". $x[1];
$c = $x[$n3k[2]];
$given[2] = " = ". $x[2];
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];





##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
 
$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[0] = ",NAMED_ANS_RULE("angle0".$trial,6)]);
        push @namedCmp , "angle0".$trial=>num_cmp( $X[0], reltol=>3  ) ; 

         $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $LL[2] = ",NAMED_ANS_RULE("angle2".$trial,6)]);
        push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ; 
 

        $table .= EndTable();}


if ($case == 6.4){   ###sss   obtuse angle

$fact = 1;
$x[0] = pop @list;

$x[1] = pop @list;

#forcing longest side longer than would-be hypotenuse vvvvvvvvvvvvvvvvv
$shortest = int (1.2 * sqrt ($x[0] **2 + $x[1]**2) +1);
$longest = $x[0] + $x[1] -2;
$x[2] = random ($shortest, $longest,1);
#forcing longest side longer than would-be hypotenuse ^^^^^^^^^^^^^^^^^^


#use cosine law to find angles
$X[0] = (180/$PI)*acos ((  $x[1]**2 + $x[2]**2- $x[0]**2)/(2*$x[1]*$x[2])); 
$X[1] = (180/$PI)*acos ((  $x[0]**2 + $x[2]**2- $x[1]**2)/(2*$x[0]*$x[2]));

$X[2] = 180 - $X[0] - $X[1] ;
for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 

$A = $X[$n3k[0]];
$Given[0] = "";
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] =" = ". $x[0];
$b = $x[$n3k[1]];
$given[1] = " = ". $x[1];
$c = $x[$n3k[2]];
$given[2] = " = ". $x[2];
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];





##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
 
$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[0] = ",NAMED_ANS_RULE("angle0".$trial,6)]);
        push @namedCmp , "angle0".$trial=>num_cmp( $X[0], reltol=>3  ) ; 

         $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $LL[2] = ",NAMED_ANS_RULE("angle2".$trial,6)]);
        push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ; 
 

        $table .= EndTable();
}




if ($case == 6.5){   ###sss   obtuse angle - small numbers
$fact = list_random(0.01,0.1,0.001);
$x[0] = pop @list;

$x[1] = pop @list;

#forcing longest side longer than would-be hypotenuse vvvvvvvvvvvvvvvvv
$shortest = int (1.2 * sqrt ($x[0] **2 + $x[1]**2) +1);
$longest = $x[0] + $x[1] -2;
$x[2] = random ($shortest, $longest,1);
#forcing longest side longer than would-be hypotenuse ^^^^^^^^^^^^^^^^^^


#use cosine law to find angles
$X[0] = (180/$PI)*acos ((  $x[1]**2 + $x[2]**2- $x[0]**2)/(2*$x[1]*$x[2])); 
$X[1] = (180/$PI)*acos ((  $x[0]**2 + $x[2]**2- $x[1]**2)/(2*$x[0]*$x[2]));

$X[2] = 180 - $X[0] - $X[1] ;
for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 


$A = $X[$n3k[0]];
$Given[0] = "";
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] =" = ". $x[0];
$b = $x[$n3k[1]];
$given[1] = " = ". $x[1];
$c = $x[$n3k[2]];
$given[2] = " = ". $x[2];
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];


##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
  
$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[0] = ",NAMED_ANS_RULE("angle0".$trial,6)]);
        push @namedCmp , "angle0".$trial=>num_cmp( $X[0], reltol=>3  ) ; 

         $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $LL[2] = ",NAMED_ANS_RULE("angle2".$trial,6)]);
        push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ; 
 

        $table .= EndTable();
}

if ($case == 6.6){   ###sss   obtuse angle - large numbers


$fact = list_random(100,1000,10000);
$x[0] = pop @list;

$x[1] = pop @list;

#forcing longest side longer than would-be hypotenuse vvvvvvvvvvvvvvvvv
$shortest = int (1.2 * sqrt ($x[0] **2 + $x[1]**2) +1);
$longest = $x[0] + $x[1] -2;
$x[2] = random ($shortest, $longest,1);
#forcing longest side longer than would-be hypotenuse ^^^^^^^^^^^^^^^^^^


#use cosine law to find angles
$X[0] = (180/$PI)*acos ((  $x[1]**2 + $x[2]**2- $x[0]**2)/(2*$x[1]*$x[2])); 
$X[1] = (180/$PI)*acos ((  $x[0]**2 + $x[2]**2- $x[1]**2)/(2*$x[0]*$x[2]));

$X[2] = 180 - $X[0] - $X[1] ;
for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 


$A = $X[$n3k[0]];
$Given[0] = "";
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] =" = ". $x[0];
$b = $x[$n3k[1]];
$given[1] = " = ". $x[1];
$c = $x[$n3k[2]];
$given[2] = " = ". $x[2];
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];





##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
  
$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[0] = ",NAMED_ANS_RULE("angle0".$trial,6)]);
        push @namedCmp , "angle0".$trial=>num_cmp( $X[0], reltol=>3  ) ; 

         $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $LL[2] = ",NAMED_ANS_RULE("angle2".$trial,6)]);
        push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ; 
 

        $table .= EndTable();}

if ($case == 6.7){   ###sss   obtuse angle - scientific notation


$fact = list_random(10**50,10**20,10**-23,10**-24);
$x[0] = pop @list;

$x[1] = pop @list;

#forcing longest side longer than would-be hypotenuse vvvvvvvvvvvvvvvvv
$shortest = int (1.2 * sqrt ($x[0] **2 + $x[1]**2) +1);
$longest = $x[0] + $x[1] -2;
$x[2] = random ($shortest, $longest,1);
#forcing longest side longer than would-be hypotenuse ^^^^^^^^^^^^^^^^^^


#use cosine law to find angles
$X[0] = (180/$PI)*acos ((  $x[1]**2 + $x[2]**2- $x[0]**2)/(2*$x[1]*$x[2])); 
$X[1] = (180/$PI)*acos ((  $x[0]**2 + $x[2]**2- $x[1]**2)/(2*$x[0]*$x[2]));

$X[2] = 180 - $X[0] - $X[1] ;
for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 


$A = $X[$n3k[0]];
$Given[0] = "";
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] =" = ". $x[0];
$b = $x[$n3k[1]];
$given[1] = " = ". $x[1];
$c = $x[$n3k[2]];
$given[2] = " = ". $x[2];
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];





##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
   
$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[0] = ",NAMED_ANS_RULE("angle0".$trial,6)]);
        push @namedCmp , "angle0".$trial=>num_cmp( $X[0], reltol=>3  ) ; 

         $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $LL[2] = ",NAMED_ANS_RULE("angle2".$trial,6)]);
        push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ; 
 

        $table .= EndTable();}









if ($case == 7){   ###sas acute angle#vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv

$fact = 1;
$x[0] = pop @list;
$x[1] = pop @list;
$X[2] = pop @AcuteList;

$x[2] = sqrt ($x[0]**2 + $x[1]**2 - 2 * $x[0] * $x[1] * cos($PI / 180 * $X[2]));
#use cosine law to find angles
$X[0] = (180/$PI)*acos ((  $x[1]**2 + $x[2]**2 - $x[0]**2)/(2*$x[1]*$x[2])); 
$X[1] = (180/$PI)*acos ((  $x[0]**2 + $x[2]**2 - $x[1]**2)/(2*$x[0]*$x[2]));
for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 




$A = $X[$n3k[0]];
$Given[0] = "";
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "=". $X[2].$deg;
$a = $x[$n3k[0]];
$given[0] = "= ". $x[0];
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];

##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
   
$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[0] = ",NAMED_ANS_RULE("angle0".$trial,6)]);
        push @namedCmp , "angle0".$trial=>num_cmp( $X[0], reltol=>3  ) ; 

         $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("side2".$trial,6)]);
        push @namedCmp , "side2".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 

        $table .= EndTable();








}   #^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^


if ($case == 7.1){   ###sas acute angle#vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv

$fact = list_random(0.01,0.1,0.001);
$x[0] = pop @list;
$x[1] = pop @list;
$X[2] = pop @AcuteList;

$x[2] = sqrt ($x[0]**2 + $x[1]**2 - 2 * $x[0] * $x[1] * cos($PI / 180 * $X[2]));
#use cosine law to find angles
$X[0] = (180/$PI)*acos ((  $x[1]**2 + $x[2]**2 - $x[0]**2)/(2*$x[1]*$x[2])); 
$X[1] = (180/$PI)*acos ((  $x[0]**2 + $x[2]**2 - $x[1]**2)/(2*$x[0]*$x[2]));
for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 




$A = $X[$n3k[0]];
$Given[0] = "";
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "=". $X[2].$deg;
$a = $x[$n3k[0]];
$given[0] = "= ". $x[0];
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];

##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
  
$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[0] = ",NAMED_ANS_RULE("angle0".$trial,6)]);
        push @namedCmp , "angle0".$trial=>num_cmp( $X[0], reltol=>3  ) ; 

         $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("side2".$trial,6)]);
        push @namedCmp , "side2".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 

        $table .= EndTable();








}   #^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

if ($case == 7.2){   ###sas acute angle#vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv

$fact = list_random(1000,100,10000);
$x[0] = pop @list;
$x[1] = pop @list;
$X[2] = pop @AcuteList;

$x[2] = sqrt ($x[0]**2 + $x[1]**2 - 2 * $x[0] * $x[1] * cos($PI / 180 * $X[2]));
#use cosine law to find angles
$X[0] = (180/$PI)*acos ((  $x[1]**2 + $x[2]**2 - $x[0]**2)/(2*$x[1]*$x[2])); 
$X[1] = (180/$PI)*acos ((  $x[0]**2 + $x[2]**2 - $x[1]**2)/(2*$x[0]*$x[2]));
for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 




$A = $X[$n3k[0]];
$Given[0] = "";
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "=". $X[2].$deg;
$a = $x[$n3k[0]];
$given[0] = "= ". $x[0];
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];

##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
  
$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[0] = ",NAMED_ANS_RULE("angle0".$trial,6)]);
        push @namedCmp , "angle0".$trial=>num_cmp( $X[0], reltol=>3  ) ; 

         $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("side2".$trial,6)]);
        push @namedCmp , "side2".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 

        $table .= EndTable();








}   #^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

if ($case == 7.3){   ###sas acute angle#vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv

$fact = list_random(10**20,10**40,10**21,10**-20,10**-30,10**-31);
$x[0] = pop @list;
$x[1] = pop @list;
$X[2] = pop @AcuteList;

$x[2] = sqrt ($x[0]**2 + $x[1]**2 - 2 * $x[0] * $x[1] * cos($PI / 180 * $X[2]));
#use cosine law to find angles
$X[0] = (180/$PI)*acos ((  $x[1]**2 + $x[2]**2 - $x[0]**2)/(2*$x[1]*$x[2])); 
$X[1] = (180/$PI)*acos ((  $x[0]**2 + $x[2]**2 - $x[1]**2)/(2*$x[0]*$x[2]));
for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 




$A = $X[$n3k[0]];
$Given[0] = "";
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "=". $X[2].$deg;
$a = $x[$n3k[0]];
$given[0] = "= ". $x[0];
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];

##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
  
$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[0] = ",NAMED_ANS_RULE("angle0".$trial,6)]);
        push @namedCmp , "angle0".$trial=>num_cmp( $X[0], reltol=>3  ) ; 

         $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("side2".$trial,6)]);
        push @namedCmp , "side2".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 

        $table .= EndTable();








}   #^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^




if ($case == 8){   ###sas obtuse ###vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
$fact = 1;
$x[0] = pop @list;
$x[1] = pop @list;
$X[2] = pop @ObtuseList;

$x[2] = sqrt ($x[0]**2 + $x[1]**2 - 2 * $x[0] * $x[1] * cos($PI / 180 * $X[2]));
#use cosine law to find angles
$X[0] = (180/$PI)*acos ((  $x[1]**2 + $x[2]**2 - $x[0]**2)/(2*$x[1]*$x[2])); 
$X[1] = (180/$PI)*acos ((  $x[0]**2 + $x[2]**2 - $x[1]**2)/(2*$x[0]*$x[2]));
for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 



$A = $X[$n3k[0]];
$Given[0] = "";
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "= ". $X[2].$deg;
$a = $x[$n3k[0]];
$given[0] = "= ". $x[0];
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];


##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
    
$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[0] = ",NAMED_ANS_RULE("angle0".$trial,6)]);
        push @namedCmp , "angle0".$trial=>num_cmp( $X[0], reltol=>3  ) ; 

         $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("side2".$trial,6)]);
        push @namedCmp , "side2".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 

        $table .= EndTable();




}    #   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

if ($case == 8.1){   ###sas obtuse ###vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
$fact = list_random(0.1,0.01,0.001);
$x[0] = pop @list;
$x[1] = pop @list;
$X[2] = pop @ObtuseList;

$x[2] = sqrt ($x[0]**2 + $x[1]**2 - 2 * $x[0] * $x[1] * cos($PI / 180 * $X[2]));
#use cosine law to find angles
$X[0] = (180/$PI)*acos ((  $x[1]**2 + $x[2]**2 - $x[0]**2)/(2*$x[1]*$x[2])); 
$X[1] = (180/$PI)*acos ((  $x[0]**2 + $x[2]**2 - $x[1]**2)/(2*$x[0]*$x[2]));
for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 



$A = $X[$n3k[0]];
$Given[0] = "";
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "= ". $X[2].$deg;
$a = $x[$n3k[0]];
$given[0] = "= ". $x[0];
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];


##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
  
$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[0] = ",NAMED_ANS_RULE("angle0".$trial,6)]);
        push @namedCmp , "angle0".$trial=>num_cmp( $X[0], reltol=>3  ) ; 

         $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("side2".$trial,6)]);
        push @namedCmp , "side2".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 

        $table .= EndTable();




}    #   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

if ($case == 8.2){   ###sas obtuse ###vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
$fact = list_random(100,1000,10000);
$x[0] = pop @list;
$x[1] = pop @list;
$X[2] = pop @ObtuseList;

$x[2] = sqrt ($x[0]**2 + $x[1]**2 - 2 * $x[0] * $x[1] * cos($PI / 180 * $X[2]));
#use cosine law to find angles
$X[0] = (180/$PI)*acos ((  $x[1]**2 + $x[2]**2 - $x[0]**2)/(2*$x[1]*$x[2])); 
$X[1] = (180/$PI)*acos ((  $x[0]**2 + $x[2]**2 - $x[1]**2)/(2*$x[0]*$x[2]));
for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 



$A = $X[$n3k[0]];
$Given[0] = "";
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "= ". $X[2].$deg;
$a = $x[$n3k[0]];
$given[0] = "= ". $x[0];
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];


##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
   
$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[0] = ",NAMED_ANS_RULE("angle0".$trial,6)]);
        push @namedCmp , "angle0".$trial=>num_cmp( $X[0], reltol=>3  ) ; 

         $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("side2".$trial,6)]);
        push @namedCmp , "side2".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 

        $table .= EndTable();




}    #   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

if ($case == 8.3){   ###sas obtuse ###vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
$fact = list_random(10**40,10**90,10**-30,10**-35);
$x[0] = pop @list;
$x[1] = pop @list;
$X[2] = pop @ObtuseList;

$x[2] = sqrt ($x[0]**2 + $x[1]**2 - 2 * $x[0] * $x[1] * cos($PI / 180 * $X[2]));
#use cosine law to find angles
$X[0] = (180/$PI)*acos ((  $x[1]**2 + $x[2]**2 - $x[0]**2)/(2*$x[1]*$x[2])); 
$X[1] = (180/$PI)*acos ((  $x[0]**2 + $x[2]**2 - $x[1]**2)/(2*$x[0]*$x[2]));
for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact} 



$A = $X[$n3k[0]];
$Given[0] = "";
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "= ". $X[2].$deg;
$a = $x[$n3k[0]];
$given[0] = "= ". $x[0];
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];


##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
   
$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[0] = ",NAMED_ANS_RULE("angle0".$trial,6)]);
        push @namedCmp , "angle0".$trial=>num_cmp( $X[0], reltol=>3  ) ; 

         $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("side2".$trial,6)]);
        push @namedCmp , "side2".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 

        $table .= EndTable();




}    #   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^



if ($case == 9){   ###ass acute

$fact = 1;

$x[1] = pop @list;
$X[0] = pop @SmallAcuteList;


# for the other given side vvvvvvvvvvv
$minLength = int( 1.1 *$x[1]* sin ($PI / 180 * $X[0]) + 1);
$maxLength = int(0.7 * $x[1]);
$x[0] = random ($minLength, $maxLength);
#for the other given side ^^^^^^^^^^^^

$X[1] = 180 / $PI * asin(sin ($PI / 180 * $X[0]) / $x[0] * $x[1]);
$X[2] = 180 - $X[0] - $X[1];
$x[2] = sqrt($x[0]**2 + $x[1]**2 - 2 * $x[0]*$x[1] *  cos($PI / 180 * $X[2]));

for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact}


$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "(acute)";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "= ". $x[0];
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];

##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
  
$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 

         $table .= AlignedRow([" $LL[2] = ",NAMED_ANS_RULE("angle2".$trial,6)]);
        push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("side2".$trial,6)]);
        push @namedCmp , "side2".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 

        $table .= EndTable();


}



if ($case == 9.1){   ###ass acute

$fact = list_random(0.1,.001,.0001);

$x[1] = pop @list;
$X[0] = pop @SmallAcuteList;


# for the other given side vvvvvvvvvvv
$minLength = int( 1.1 *$x[1]* sin ($PI / 180 * $X[0]) + 1);
$maxLength = int(0.7 * $x[1]);
$x[0] = random ($minLength, $maxLength);
#for the other given side ^^^^^^^^^^^^

$X[1] = 180 / $PI * asin(sin ($PI / 180 * $X[0]) / $x[0] * $x[1]);
$X[2] = 180 - $X[0] - $X[1];
$x[2] = sqrt($x[0]**2 + $x[1]**2 - 2 * $x[0]*$x[1] *  cos($PI / 180 * $X[2]));

for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact}


$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "(acute)";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "= ". $x[0];
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];

##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
   
$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 

         $table .= AlignedRow([" $LL[2] = ",NAMED_ANS_RULE("angle2".$trial,6)]);
        push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("side2".$trial,6)]);
        push @namedCmp , "side2".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 

        $table .= EndTable();


}
if ($case == 9.2){   ###ass acute

$fact = list_random(1000,10,100);

$x[1] = pop @list;
$X[0] = pop @SmallAcuteList;


# for the other given side vvvvvvvvvvv
$minLength = int( 1.1 *$x[1]* sin ($PI / 180 * $X[0]) + 1);
$maxLength = int(0.7 * $x[1]);
$x[0] = random ($minLength, $maxLength);
#for the other given side ^^^^^^^^^^^^

$X[1] = 180 / $PI * asin(sin ($PI / 180 * $X[0]) / $x[0] * $x[1]);
$X[2] = 180 - $X[0] - $X[1];
$x[2] = sqrt($x[0]**2 + $x[1]**2 - 2 * $x[0]*$x[1] *  cos($PI / 180 * $X[2]));

for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact}


$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "(acute)";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "= ". $x[0];
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];

##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
  
$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 

         $table .= AlignedRow([" $LL[2] = ",NAMED_ANS_RULE("angle2".$trial,6)]);
        push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("side2".$trial,6)]);
        push @namedCmp , "side2".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 

        $table .= EndTable();


}
if ($case == 9.3){   ###ass acute

$fact = list_random(10**40,10**41,10**-30,10**-40);

$x[1] = pop @list;
$X[0] = pop @SmallAcuteList;


# for the other given side vvvvvvvvvvv
$minLength = int( 1.1 *$x[1]* sin ($PI / 180 * $X[0]) + 1);
$maxLength = int(0.7 * $x[1]);
$x[0] = random ($minLength, $maxLength);
#for the other given side ^^^^^^^^^^^^

$X[1] = 180 / $PI * asin(sin ($PI / 180 * $X[0]) / $x[0] * $x[1]);
$X[2] = 180 - $X[0] - $X[1];
$x[2] = sqrt($x[0]**2 + $x[1]**2 - 2 * $x[0]*$x[1] *  cos($PI / 180 * $X[2]));

for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact}


$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "(acute)";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "= ". $x[0];
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];

##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
  
$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 

         $table .= AlignedRow([" $LL[2] = ",NAMED_ANS_RULE("angle2".$trial,6)]);
        push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("side2".$trial,6)]);
        push @namedCmp , "side2".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 

        $table .= EndTable();


}

if ($case == 10){   ###ass obtuse

$fact = 1;
$x[1] = pop @list;
$X[0] = pop @SmallAcuteList;


# for the other given side vvvvvvvvvvv
$minLength = int( 1.1 *$x[1]* sin ($PI / 180 * $X[0]) + 1);
$maxLength = int(0.7 * $x[1]);
$x[0] = random ($minLength, $maxLength);
#for the other given side ^^^^^^^^^^^^

$X[1] = 180 - (180 / $PI) * asin(sin ($PI / 180 * $X[0]) / $x[0] * $x[1]);
$X[2] = 180 - $X[0] - $X[1];
$x[2] = sqrt($x[0]**2 + $x[1]**2 - 2 * $x[0]*$x[1] *  cos($PI / 180 * $X[2]));

for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact}






$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "(obtuse)";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "= ". $x[0];
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];

##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
   
$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 

         $table .= AlignedRow([" $LL[2] = ",NAMED_ANS_RULE("angle2".$trial,6)]);
        push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("side2".$trial,6)]);
        push @namedCmp , "side2".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 

        $table .= EndTable();


}

if ($case == 10.1){   ###ass obtuse small sides

$fact = list_random(0.1,0.01,0.001);
$x[1] = pop @list;
$X[0] = pop @SmallAcuteList;


# for the other given side vvvvvvvvvvv
$minLength = int( 1.1 *$x[1]* sin ($PI / 180 * $X[0]) + 1);
$maxLength = int(0.7 * $x[1]);
$x[0] = random ($minLength, $maxLength);
#for the other given side ^^^^^^^^^^^^

$X[1] = 180 - (180 / $PI) * asin(sin ($PI / 180 * $X[0]) / $x[0] * $x[1]);
$X[2] = 180 - $X[0] - $X[1];
$x[2] = sqrt($x[0]**2 + $x[1]**2 - 2 * $x[0]*$x[1] *  cos($PI / 180 * $X[2]));

for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact}





$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "(obtuse)";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "= ". $x[0];
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];


##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
 
$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 

         $table .= AlignedRow([" $LL[2] = ",NAMED_ANS_RULE("angle2".$trial,6)]);
        push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("side2".$trial,6)]);
        push @namedCmp , "side2".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 

        $table .= EndTable();



}

if ($case == 10.2){   ###ass obtuse

$fact = list_random(1000,100,10000);
$x[1] = pop @list;
$X[0] = pop @SmallAcuteList;


# for the other given side vvvvvvvvvvv
$minLength = int( 1.1 *$x[1]* sin ($PI / 180 * $X[0]) + 1);
$maxLength = int(0.7 * $x[1]);
$x[0] = random ($minLength, $maxLength);
#for the other given side ^^^^^^^^^^^^

$X[1] = 180 - (180 / $PI) * asin(sin ($PI / 180 * $X[0]) / $x[0] * $x[1]);
$X[2] = 180 - $X[0] - $X[1];
$x[2] = sqrt($x[0]**2 + $x[1]**2 - 2 * $x[0]*$x[1] *  cos($PI / 180 * $X[2]));

for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact}







$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "(obtuse)";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "= ". $x[0];
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];
##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv

$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 

         $table .= AlignedRow([" $LL[2] = ",NAMED_ANS_RULE("angle2".$trial,6)]);
        push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("side2".$trial,6)]);
        push @namedCmp , "side2".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 

        $table .= EndTable();



}


if ($case == 10.3){   ###ass obtuse

$fact = list_random(10**40,10**50,10**-90,10**-81);
$x[1] = pop @list;
$X[0] = pop @SmallAcuteList;


# for the other given side vvvvvvvvvvv
$minLength = int( 1.1 *$x[1]* sin ($PI / 180 * $X[0]) + 1);
$maxLength = int(0.7 * $x[1]);
$x[0] = random ($minLength, $maxLength);
#for the other given side ^^^^^^^^^^^^

$X[1] = 180 - (180 / $PI) * asin(sin ($PI / 180 * $X[0]) / $x[0] * $x[1]);
$X[2] = 180 - $X[0] - $X[1];
$x[2] = sqrt($x[0]**2 + $x[1]**2 - 2 * $x[0]*$x[1] *  cos($PI / 180 * $X[2]));

for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact}






$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "(obtuse)";
$C = $X[$n3k[2]];
$Given[2] = "";
$a = $x[$n3k[0]];
$given[0] = "= ". $x[0];
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];

##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
 
$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 

         $table .= AlignedRow([" $LL[2] = ",NAMED_ANS_RULE("angle2".$trial,6)]);
        push @namedCmp , "angle2".$trial=>num_cmp( $X[2], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("side2".$trial,6)]);
        push @namedCmp , "side2".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 

        $table .= EndTable();



}








if ($case == 11){   ###asa 


$fact = 1;
# given vvvvvvvvvvvvvvv
$x[1] = pop @list;
$X[0] = pop @SmallAcuteList;

$X[2] = random(30,160 - $X[0],5);
# given ^^^^^^^^^^^^^^^^^^^^^^


$X[1] = 180 - $X[0] - $X[2] ;
$x[2] = sin ($PI / 180 * $X[2]) * $x[1]  / sin ($PI / 180 * $X[1]);
$x[0] = sin ($PI / 180 * $X[0]) * $x[1]  / sin ($PI / 180 * $X[1]);


for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact}




$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "=".$X[2].$deg;
$a = $x[$n3k[0]];
$given[0] = "";
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];


##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
    
$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 

         $table .= AlignedRow([" $ll[0] = ",NAMED_ANS_RULE("side0".$trial,6)]);
        push @namedCmp , "side0".$trial=>num_cmp( $x[0], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("side2".$trial,6)]);
        push @namedCmp , "side2".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 

        $table .= EndTable();
}



if ($case == 11.1){   ###asa 


$fact = list_random(0.01,0.001,0.0001);
# given vvvvvvvvvvvvvvv
$x[1] = pop @list;
$X[0] = pop @SmallAcuteList;

$X[2] = random(30,160 - $X[0],5);
# given ^^^^^^^^^^^^^^^^^^^^^^


$X[1] = 180 - $X[0] - $X[2] ;
$x[2] = sin ($PI / 180 * $X[2]) * $x[1]  / sin ($PI / 180 * $X[1]);
$x[0] = sin ($PI / 180 * $X[0]) * $x[1]  / sin ($PI / 180 * $X[1]);


for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact}




$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "=".$X[2].$deg;
$a = $x[$n3k[0]];
$given[0] = "";
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];


##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
 
$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 

         $table .= AlignedRow([" $ll[0] = ",NAMED_ANS_RULE("side0".$trial,6)]);
        push @namedCmp , "side0".$trial=>num_cmp( $x[0], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("side2".$trial,6)]);
        push @namedCmp , "side2".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 

        $table .= EndTable();
}




if ($case == 11.2){   ###asa 


$fact = list_random(100,1000,10000);
# given vvvvvvvvvvvvvvv
$x[1] = pop @list;
$X[0] = pop @SmallAcuteList;

$X[2] = random(30,160 - $X[0],5);
# given ^^^^^^^^^^^^^^^^^^^^^^


$X[1] = 180 - $X[0] - $X[2] ;
$x[2] = sin ($PI / 180 * $X[2]) * $x[1]  / sin ($PI / 180 * $X[1]);
$x[0] = sin ($PI / 180 * $X[0]) * $x[1]  / sin ($PI / 180 * $X[1]);


for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact}




$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "=".$X[2].$deg;
$a = $x[$n3k[0]];
$given[0] = "";
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];


##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
   
$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 

         $table .= AlignedRow([" $ll[0] = ",NAMED_ANS_RULE("side0".$trial,6)]);
        push @namedCmp , "side0".$trial=>num_cmp( $x[0], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("side2".$trial,6)]);
        push @namedCmp , "side2".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 

        $table .= EndTable();
}



if ($case == 11.3){   ###asa 


$fact = list_random(10**50,10**51,10**-50,10**-51);
# given vvvvvvvvvvvvvvv
$x[1] = pop @list;
$X[0] = pop @SmallAcuteList;

$X[2] = random(30,160 - $X[0],5);
# given ^^^^^^^^^^^^^^^^^^^^^^


$X[1] = 180 - $X[0] - $X[2] ;
$x[2] = sin ($PI / 180 * $X[2]) * $x[1]  / sin ($PI / 180 * $X[1]);
$x[0] = sin ($PI / 180 * $X[0]) * $x[1]  / sin ($PI / 180 * $X[1]);


for ($i = 0; $i <3; $i++) {$x[$i] *=   $fact}




$A = $X[$n3k[0]];
$Given[0] = "= ". $X[0].$deg;
$B = $X[$n3k[1]];
$Given[1] = "";
$C = $X[$n3k[2]];
$Given[2] = "=".$X[2].$deg;
$a = $x[$n3k[0]];
$given[0] = "";
$b = $x[$n3k[1]];
$given[1] = "= ". $x[1];
$c = $x[$n3k[2]];
$given[2] = "";
$Alabel = $AL.$Given[$n3k[0]];
$Blabel = $BL.$Given[$n3k[1]];
$Clabel = $CL.$Given[$n3k[2]];
$alabel = $aL.$given[$n3k[0]];
$blabel = $bL.$given[$n3k[1]];
$clabel = $cL.$given[$n3k[2]];


##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
 
$table = BeginTable(spacing => 3);

        $table .= AlignedRow([" $LL[1] = ",NAMED_ANS_RULE("angle1".$trial,6)]);
        push @namedCmp , "angle1".$trial=>num_cmp( $X[1], reltol=>3  ) ; 

         $table .= AlignedRow([" $ll[0] = ",NAMED_ANS_RULE("side0".$trial,6)]);
        push @namedCmp , "side0".$trial=>num_cmp( $x[0], reltol=>3  ) ; 
 
         $table .= AlignedRow([" $ll[2] = ",NAMED_ANS_RULE("side2".$trial,6)]);
        push @namedCmp , "side2".$trial=>num_cmp( $x[2], reltol=>3  ) ; 
 

        $table .= EndTable();
}




$AX = $b * cos ($PI * $C / 180);
$AY = $b * sin ($PI * $C / 180);


$dimX = max (max ($a, $a - $AX),  $AX);
$dimY = $AY ;
$size = 1.5 * max ($dimX, $dimY);
$marginX = 0.5 * ($size - $dimX);
$marginY = 0.5 * ($size - $AY);

$xmin = min(0,$AX ) -  $marginX;
$xmax = $size + $xmin;
$ymin = -1 * $marginY;
$ymax = $size - $marginY;



$xPixels = 600;
$yPixels = 600;


$pic = init_graph($xmin,$ymin,$xmax,$ymax,'pixels'=>[$xPixels,$yPixels]);


$lab=new Label(0,0,$Clabel,'black','top','center');
$pic->lb($lab);

$lab=new Label($AX,$AY,$Alabel,'black','bottom','left');
$pic->lb($lab);

$lab=new Label($a,0,$Blabel);
$pic->lb($lab);

$lab=new Label($a/2,0,$alabel,'black','center','top');
$pic->lb($lab);

$lab=new Label($AX/2- abs(0.03 *$a),$AY/2,$blabel,'black','right','bottom');
$pic->lb($lab);

$lab=new Label(($AX + $a) / 2 + abs(0.03 *$a), $AY /2 ,$clabel, 'black','left','bottom');
$pic->lb($lab);

  $pic->new_color("lightblue", 214,230,244);
$pic->moveTo(0,0);
$pic->lineTo($AX,$AY,1);
$pic->lineTo($a,0,1);
$pic->lineTo(0,0,1);
$pic->fillRegion([($a / 2 + $AX)/2,$AY/2,'lightblue']);





BEGIN_TEXT

$HR $HR Number $trial $BR 

\{ image(insertGraph($pic), width=>$xPixels, height=>$yPixels) \}


$PAR
$table


END_TEXT

NAMED_ANS(@namedCmp);



}
TEXT($END_ONE_COLUMN);
ENDDOCUMENT();