Finding distance using Angles and Sine

Question

Two weather tracking stations are on the equator 159 miles apart. A weather balloon is located on a bearing of North 38 degrees East from the station and on a bearing of North 14 degrees from the eastern station. How far is the balloon from the western station?

Answer 1

From what I can surmise from the tracking stations and the weather balloon, we have a triangulation going on. A triangle has formed between the two tracking stations & the weather balloon with angles of 38º, 14º, and lastly 128º. To find the distance between the weather balloon & the western station, we must use the law of sines.

 

a/sin A = b/sin B = c/sin C

 

In this case a = 159 (the distance between the stations) & A = 128º (the angle opposite this distance). We need to find b (distance between the western station & the balloon), and we already know B = 14º

 

159/sin 128º = b/sin 14º

 

b = 159 * sin 14º/sin 128º = 48.81 miles