## DESCRIPTION
## Precalculus: Trigonometry
## ENDDESCRIPTION

## KEYWORDS('trigonometry')
## Tagged by cmd6a 6/22/06

## DBsubject('Trigonometry')
## DBchapter('Trigonometric Functions Of Angles')
## DBsection('The Law of Cosines')
## Date('')
## Author('')
## Institution('ASU')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl",
"PGasu.pl"
);

TEXT(beginproblem());

#
# Now we do the randomization of variables, and other computations
# as needed for this problem.  Sometimes we compute the answers here.
#

$a = random(4,9);
$pi=4*atan(1);
$angC=random(40,120,10);  #angle C in degrees
$dC=$angC*$pi/180;  #angle C in radians
$angA=random(25,55,5);  #angle A in degrees
$dA=$angA*$pi/180;  #angle A in radians

#ANSWERS
$angB = 180-$angA-$angC;
$dB=$angB*$pi/180;
$ans1=$angB;
$b=$a*sin($dB)/sin($dA);
$ans2 = $b;
$c=$a*sin($dC)/sin($dA);
$ans3 = $c;


BEGIN_TEXT
Consider the triangle below. Click on the picture to see it more clearly.
$BR
\{ image("triangle.gif") \}
$BR
If \( a=$a \), the angle \( C=$angC ^\circ \) and the angle
\( A=$angA ^\circ \)  find the other angle \(B\) and the remaining sides \(b\) and
\(c\). Give your answer to at least 3 decimal places.

    $PAR
$BR \(B =\) \{ans_rule(20)\} degrees
$BR     \(b =\) \{ans_rule(20)\}
$BR     \(c =\) \{ans_rule(20)\}
        
END_TEXT

#
# Tell WeBWork how to test if answers are right.  These should come in the
# same order as the answer blanks above.  You tell WeBWork both the type of
# "answer evaluator" to use, and the correct answer.
#

ANS(num_cmp($ans1));
ANS(num_cmp($ans2));
ANS(num_cmp($ans3));

ENDDOCUMENT();        # This should be the last executable line in the problem.