Math CentralQuandaries & Queries


Question from Christine, a student:

A, B and C are three towns, the bearing of B and C from A being 310 degrees and 220 degrees, and their distances from A are 510km and 700km respectively. Find the bearing of B from C to the nearest minute.

This question cannot be answered as stated, because the earth is a sphere, and the answer depends significantly on the location of town A. If A is very close to the North Pole, the bearing will be nearly 70 degrees; if we imagine A moving southward, the bearing increases to about 180 degrees near the equator and to almost 250 degrees near the South Pole. Moreover, the two legs are long enough (around five degrees of great-circle arc) that the non-Euclidean geometry of the triangle must be taken into account if you want 1 minute accuracy.

If we assume the Earth to be flat (as I'm afraid you are meant to) the problem becomes a lot easier - especially when you note what the angle $\angle BAC$ is. Draw a reasonably accurate diagram and give it a try.

Good Hunting!

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