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faralatir · Jul 11, 2010, 06:11 PM

A ship A is at a distancef 6.7km and at a bearing of 308 from a lighthouse. A ship B is at a distance of 803km and at a bearing of 074 from the lighthouse. Calculate the distance AB and the bearing of B from A.

ebaines · Jul 12, 2010, 07:14 AM

The first part of the question (distance A to B) can be solved using the law of cosines. Let a = length A to the light house, b = length B to the lighthouse, and c = length A to B, then:

$<br /> c^2 = a^2 + b^2 - 2 ab \ cos (c)<br />$

where $\theta$ is the angle between a and b (which you can determine from the bearings you were given).

Then you can use the law of sines to solve the second part of the problem - fro example you can find the angle between a and c:

angle ac = length b * angle ab/c