SOLUTION: an airplane took off from the airport and started flying toward its destination 210 miles due east. After flying 80 miles east, it encountered a storm and altered its course by tur

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Question 925918: an airplane took off from the airport and started flying toward its destination 210 miles due east. After flying 80 miles east, it encountered a storm and altered its course by turning left 22'. when it was past the storm , it turned right 30'and flew in a straight line until it reached its destination. how far was the plane from its destination when it made the 30' turn ?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Here is a sketch that illustrates the situation. (The angles and proportions are not right on purpose).
The plane was 210-80=130 miles from its destination when it made the first %2822%5Eo%29 turn.
It was x miles from its destination when it made the second %2830%5Eo%29 turn.
We can use law of sines on the triangle you can see in the sketch.
The angle at the top of that triangle is the supplementary angle to the 30%5Eo angle of the second turn.
It measures 180%5Eo-30%5Eo=150%5Eo , and like all supplementary angles, has the same sine:
sin%28150%5Eo%29=sin%2830%5Eo%29=0.5 (an exact 0.5=1%2F2 number).
Law of sines says that
130%2Fsin%28150%5Eo%29=x%2Fsin%2822%5Eo%29
We use sin%2822%5Eo%29=0.3746 (rounded) to get a very accurate answer.
130%2Fsin%28150%5Eo%29=x%2Fsin%2822%5Eo%29
130%2F0.5=x%2F0.3746--->130%2A0.3746%2F0.5=x--->highlight%28x=97.4%29 (rounded).
The plane was highlight%2897.4%29 miles from its destination when it made the 30%5Eo turn.