Homework Help: Can't understand trig problem

Posted by joel on Monday, February 1, 2010 at 12:45pm.

An airplane left an airport and flew east 174 miles. Then it turned northward flying along a bearing of N22E. When it was 254 miles from the airport, there was an engine problem and it turned back to take the shortest route possible back to the airport. Find theta, the angle through which the plane turned

Is the angle 39.43?

Can't understand trig problem - tom, Monday, February 1, 2010 at 1:18pm
Your answer is right
Correction - Reiny, Monday, February 1, 2010 at 3:43pm
Your answer is not correct.
I see a triangle with sides 174 and 254 and the angle between those sides as 112º.

Let the third side be x. (The return path)
By Cosine Law:
x^2 = 174^2 + 254^2 - 2(174)(254)cos112º
x = 357.637

Let the angle at the turn be ß
By Sine Law:
sin ß/174 = sin 112/357.637
sin ß = .4510998
ß = 26.8º

So the plane must turn an angle of (180-26.8) or 153.2º

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