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.

Answer 2

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

M (ABP) = 39.17° + 90° = 129.17°

What is bearing?

It is an element that constrains relative motion to only the desired motion and reduces friction between moving parts.

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

AP²= BP² + BA² - 2 x BP x BA x cos = 219.17

AP² =150² + 120² - 2 x 150 x 120 x (-0.63)

AP² = 22500 + 14400 + 22680 = 59580

AP = +√59580 = 244 miles

Learn more about bearing here:

https://brainly.com/question/23427938