Two tracking stations are on the equator 135 miles apart. A weather balloon is located on a bearing of N 37 degrees E from the weastern station and on a bearing of N 19 degrees E from the eastern station. How far is the balloon from the weastern station?

Answer 1

If we draw a triangle WBE with the obvious labels for angles and sides, we have angles

W=53 degrees
E=109 degrees
B=18 degrees

Now, using the law of sines

w/sin109 = 135/sin18
w=413 miles