Hi! Can someone please confirm my answer. Thank you.
Two weather tracking stations are on the equator 146 miles apart. A weather balloon is located on a bearing of N 35°E from the western station and on a bearing of N 23°E from the eastern station. How far is the balloon from the western station?

Question

Hi! Can someone please confirm my answer. Thank you. 
Two weather tracking stations are on the equator 146 miles apart. A weather balloon is located on a bearing of N 35°E from the western station and on a bearing of N 23°E from the eastern station. How far is the balloon from the western station?

mathmale · Answer

I'd need to see how you obtained your answer to give you feedback on it.
Are you using the concept of "arc length" here?

mathmale · Answer

OK.  The earth's surface is curved, as you well know, but for relatively short distances we could assume we're to find the straight line distance from one point to another.  In this type of problem, a sketch of the situation could be very useful.

mathmale · Answer

Without actually having done the problem myself, I could say that what you have done shows competence in applying the Law of Sines.     One way in which you could check your own work (which is always a good idea) would be to pretend that the distance you've found is the only one known, forgetting about the 146 miles.  Re-applying the Law of Sines, could you now obtain the distance 146 miles?

goldie1962 · Answer

Hey it worked! THANKS!!