Finding approximate latitude/longitude to the nearest minute (trigonometric)

Hello, this is my first post here on *mathhelpforum*. I hope to become an active member, helping and posting whatever I can/know to contribute.

I have been working on a problem that gives me three locations: A B and C. I have the latitude and longitude of A and B (approximate), and I have the degrees in which the directions of A B and C are pointing. By using a latitude and longitude to miles converter, I was able to find the length of side c, and since I had an opposite angle, I was able to use the Law of Sines to find the other sides, thus forming a triangle with all sides abc and angles ABC.

So I have the latitude and longitude of A (N46, W115.5), and the latitude and longitude of B (N48.16, W118.75).

A=35.83 degrees

B=54.16 degrees

C=90.01 degrees

a=125.20 miles

b=173.83 miles

c=213.87 miles

Given the information, what is the best way to approach finding the latitude and longitude of C to the nearest minute? I was guessing I could make a coordinate system, treating west as X and north as Y... I have those plotted... and do not know where to go from there.

Any help pushing me towards the right direction would be greatly appreciated.

See you around! (Evilgrin)