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| 1 : | jj | 517 | ##DESCRIPTION |
| 2 : | ## Algebra: Trigonometry of right triangles | ||
| 3 : | ##ENDDESCRIPTION | ||
| 4 : | |||
| 5 : | ##KEYWORDS('algebra', 'trigonometry', 'The law of sines') | ||
| 6 : | |||
| 7 : | ## tcao , PAID on 11-24-2003 | ||
| 8 : | |||
| 9 : | ## DBsubject('Trigonometry') | ||
| 10 : | ## DBchapter('Trigonometric Functions of Angles') | ||
| 11 : | ## DBsection('The Law of Sines') | ||
| 12 : | ## Date('6/3/2002') | ||
| 13 : | ## Author('') | ||
| 14 : | ## Institution('') | ||
| 15 : | ## TitleText1('Precalculus') | ||
| 16 : | ## EditionText1('3') | ||
| 17 : | ## AuthorText1('Stewart, Redlin, Watson') | ||
| 18 : | ## Section1('6.4') | ||
| 19 : | ## Problem1('27') | ||
| 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 : | ); | ||
| 29 : | |||
| 30 : | TEXT(beginproblem()); | ||
| 31 : | $showPartialCorrectAnswers = 0; | ||
| 32 : | |||
| 33 : | $b=random(95,105,1); | ||
| 34 : | |||
| 35 : | TEXT(EV2(<<EOT)); | ||
| 36 : | A communication tower (the side CB) is located at the top (the point C) of | ||
| 37 : | a steep hill. | ||
| 38 : | The angle of inclination of the hill is 58 degrees. A guy wire is to be | ||
| 39 : | attached to the top (the point B) of the tower and to the ground (the point A), | ||
| 40 : | $b m downhill from the base of the tower (the side AC). The angle | ||
| 41 : | \( \angle BAC \) in the figure is 12 degrees. | ||
| 42 : | See the graph | ||
| 43 : | $PAR \{ image("c6s4p27.gif") \} $PAR | ||
| 44 : | $BBOLD Click on the graph to view a larger graph$EBOLD | ||
| 45 : | $BR | ||
| 46 : | Find the length of cable (the side AB) required for the guy wire. | ||
| 47 : | Your answer is \{ans_rule(15)\} m; | ||
| 48 : | $BR | ||
| 49 : | EOT | ||
| 50 : | |||
| 51 : | $ac=180-(90-58); | ||
| 52 : | $ab=180-$ac-12; | ||
| 53 : | $ans1=$b*sin($PI*$ac/180)/sin($PI*$ab/180); | ||
| 54 : | |||
| 55 : | ANS(num_cmp($ans1)); | ||
| 56 : | |||
| 57 : | ENDDOCUMENT(); # This should be the last executable line in the problem. |
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