Quandaries
and Queries 

My name is James. This is a secondary level question. I am a student. This question is about finding bearings. A boat race starts from point A, goes North to Point B, a distance of 1000 meters. The course is triangular. The bearing from point B to point C is South 70degrees West. The distance from Point B to point C is 1500 meters. Find the course bearing from C to A. I'm not sure which angle of the implied triangle to use for the I constructed a triangle with points A,B, and C. I tried to use the 

Hi James, I drew a diagram of the triangle you described and added a NorthSouth line at C. I agree that the bearing from C to A is S 71.2^{o} E. There is a good explanation of bearings at a page kept by David Levesen, a faculty member in the Department of Geology at Brooklyn College, City Uiversity of New York.
There is however a problem with your solution. In your use of the Law of Sines you have 1500/sin(70). But the side of length 1500 m is not opposite the angle at B. First you should use the Law of Cosines to find the length of CA.
Once you know CA you can use the Law of Sines to find the angle at C.
Penny 

