View of /trunk/NationalProblemLibrary/ASU-topics/setTrigApplications/p6.pg

    1 ## DESCRIPTION
    2 ## Precalculus: Trigonometry
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('trigonometry')
    6 ## Tagged by cmd6a 6/22/06
    7 
    8 ## DBsubject('Trigonometry')
    9 ## DBchapter('Trigonometric Functions of Angles')
   10 ## DBsection('The Law of Cosines')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('ASU')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGauxiliaryFunctions.pl",
   28 "PGasu.pl"
   29 );
   30 
   31 TEXT(beginproblem());
   32 
   33 #
   34 # Now we do the randomization of variables, and other computations
   35 # as needed for this problem.  Sometimes we compute the answers here.
   36 #
   37 
   38 $BC = random(200,300,5);
   39 
   40 $angB=random(95,120,2);  #angle in degrees
   41 $B=$angB*3.14159265/180;  #angle in radians
   42 $angC=random(15,30,3);  #angle C in degrees
   43 $C=$angC*3.14159265/180;  #angle C in radians
   44 
   45 #compute the answer
   46 $angA=180-$angB-$angC;
   47 $A=$angA*3.14159265/180;  #angle A in radians
   48 $ans=sin($C)*$BC/sin($A);  #evaluate distance AB
   49 
   50 
   51 
   52 BEGIN_TEXT
   53 To find the distance AB across a river, a distance \( BC=$BC \) is laid off
   54 on one side of the river. It is found that \( B=$angB ^\circ \) and
   55 \( C=$angC ^\circ \).  Find AB.
   56 $BR
   57 See the picture below. Click on the picture to see it more clearly.
   58 $BR
   59 \{ image("river.gif") \}
   60 $BR
   61 
   62 
   63     $PAR
   64 $BR AB = \{ans_rule(20)\}
   65 
   66 END_TEXT
   67 
   68 #
   69 # Tell WeBWork how to test if answers are right.  These should come in the
   70 # same order as the answer blanks above.  You tell WeBWork both the type of
   71 # "answer evaluator" to use, and the correct answer.
   72 #
   73 
   74 ANS(num_cmp($ans));
   75 
   76 ENDDOCUMENT();        # This should be the last executable line in the problem.