Question

An airplane flies 370 miles from point A to point B with a bearing of 24 degrees. It then flies 240 miles from point B to point C with a bearing of 37 degrees. Find the distance from point A to point C. Round answer to one decimal place.

Answer 1

Given:

AB = 370 miles
angle A = 24 degrees
BC = 240 miles
angle B = 37 degrees 

To determine the distance from point A to C, we can use the cosine law since we are given two angles and two sides of a regular triangle. 
The angle opposite side AC is angle B which is equal to 37 degrees. 

(AC)^2 =(AB)^2 + (BC)^2 - 2(AB)(BC)cos(B)

solve for AC:

(AC)^2 =(370)^2 + (240)^2 - 2(370)(240)cos(37) 

AC = 229.48 miles.

Therefore, the distance from point A to C is 229.5 miles.