View of /trunk/NationalProblemLibrary/ASU-topics/setTrigApplications/p10.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 $pi = 4*arctan(1);
   39 
   40 $ang1 = random(15,80,5);   # first angle in degrees
   41 $r1 = $ang1*$pi/180;       # first angle in radians
   42 $ang2 = random(20,80,5);   # second angle in degrees
   43 $r2 = $ang2*$pi/180;       # second angle in radians
   44 $speed = random(40,60,2);
   45 $t1 = random(1,3,0.1);     # time from A to B
   46 $t2 = random(1,3,0.1);     # time from B to C
   47 
   48 # find the answer
   49 
   50 $r = $r1+$r2;              # angle B
   51 $d1 = $speed*$t1;
   52 $d2 = $speed*$t2;
   53 $distance = sqrt($d1**2+$d2**2-2*$d1*$d2*cos($r));
   54 
   55 
   56 
   57 BEGIN_TEXT
   58 The bearing from city A to city B is S \( $ang1 ^\circ \)E and the bearing
   59 from city B to city C is N \( $ang2 ^\circ \)E. (See picture below where
   60 \( \alpha = $ang1 ^\circ \) and \( \beta = $ang2 ^\circ \). Click on the picture
   61 to see it more clearly).
   62 $PAR
   63 \{ image("pb15.gif") \}
   64 $PAR
   65 It takes $t1 hours for a car traveling at $speed miles per hour to go
   66 from A to B and $t2 hours to go from B to C.
   67 $BR
   68 Find the distance between city A and city C.
   69 
   70 
   71     $PAR
   72 $BR distance = \{ans_rule(20)\}
   73 
   74 
   75 END_TEXT
   76 
   77 ANS(num_cmp($distance));
   78 
   79 ENDDOCUMENT();        # This should be the last executable line in the problem.