Question

An airplane leaves an airport and flies due west 120 miles and then 150 miles in the direction S 39.17°W. How far is the plane from the airport (round to the nearest mile)? 

Answer 1

Mark the airport with A, the current position of the plane P, and the turning point B.

m(ABP)=39.17°+90°=129.17°

Given 2 sides and the measure of the angle between them, we can find the third side by the cosine law:

$AP^{2} = BP^{2} + BA^{2}-2*BP*BA*cos (129.17)$

$AP^{2} = 150^{2} + 120^{2}-2*150*120*(-0.63)$

$AP^{2} = 22500+14400+22680=59580$

$AP=+ \sqrt{59580}= 244$ (miles)

remark : cos 129.17° can be found by searching in google : cosine calculator, or using other software.