Solve the word problem

Question

Two tracking stations are on the equator 121 miles apart. A weather balloon is located on a bearing of N 38 degrees from the western station and on a bearing of n 22 degrees E from eastern station. How far is the balloon from the western station?

Answer 1

The curvature of the earth would be negligible at only 121 miles. So, we can just setup triangle WBE (where "W" is the western station, "E" is the eastern station, and "B" is the balloon. We know angle W would be 38 degrees and E would be 22 degrees. That leaves 120 degrees for angle B. If we set the distance from the western station (W) to the balloon (B) to be "x" would use the following method:

Using the Law of Sines we get: sin120/121 = sin22/x

Cross-multiplying we get: x = (sin(22)*121)/sin(120) = 52.34 miles