Two weather tracking stations are on the equator 165 miles apart. a weather balloon is located on a bearing of n 40°e from the western station and on a bearing of n 22°e from the eastern station. how far is the balloon from the western station?

The correct answer to this question is this one:

Regular triangle with :
bearing from the western station = 90° - 40° = 50°
bearing from the eastern station.= 90° + 22° = 112°

-> the third angle : 18°

Thus the distance from balloon to the western station:

x/ sin112 = 165 / sin 18