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greatwhiteshark

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May 8, 2005
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An airplane flies from city A to city B, a distance of 150 miles and then turns through an angle of 40 degrees and heads toward city c.

a) If the distance between cities A and C is 300 miles, how far is it from city B to city C?

b) Through what angle should the pilot turn at city C to return to city A?

How do I use the Law of Sines to solve such questions?
 
Hello, greatwhiteshark!

Did you make a sketch?

An airplane flies from city A to city B, a distance of 150 miles
and then turns through an angle of 40 degrees and heads toward city C.

a) If the distance between cities A and C is 300 miles, how far is it from city B to city C?

b) Through what angle should the pilot turn at city C to return to city A?
Code:
                            * C
                       *   /       The plane flies due east from A to B.
           300    *      /                   AB = 150 miles
             *         /              Then turns 40 degrees toward C.
        *            /40d             Note: angle ABC = 140 degrees.
   * - - - - - - - * - -
  A      150      B                      Distance AC = 300 miles

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

                            * C     We have this triangle to solve.
                       *   /       
        b=300     *      /            A = ______      a = _____
             *         /  a
        *        140 /                B = 140 deg     b = 300
   * - - - - - - - *-                      
  A      c=150    B                   C = ______      c = 150
. . . . . . . . . . . . .sin C . . . . sin B
Law of Sines: . ------- . = . -------
. . . . . . . . . . . . . . c . . . . . . . b

. . . . . . . . . .sin C . . . . sin140<sup>o</sup>
We have: . ------- . = . ----------
. . . . . . . . . .150 . . . . . . 300

Then: . sin C .= .0.321393805 . ---> . C . .18.75<sup>o</sup>

. . . Hence: . A .= .180<sup>o</sup> - 140<sup>o</sup> - 18.75<sup>o</sup> .= .21.25<sup>o</sup>


. . . . . . . . . . . . . a . . . . . . .b
We will use: . ------- . = . ------
. . . . . . . . . . . .sin A . . . . sin B

. . . . . . . . . . . . . . . . . . . a . . . . . . . . . 300
. . . and we have: . -------------- . = . ----------
. . . . . . . . . . . . . . . .sin 21.25<sup>o</sup> . . . . sin 140<sup>o</sup>

. . . Therefore: . a . .169.17 miles


I'll let you figure out part (b) . . .
 
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