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Airplane Related Rate Law of Cosines Problem

Airplane Problem

In this problem we have two airplanes passing over the same point (the origin), possibly at different times. You can adjust the speeds of the two planes and the time since they were at the origin. You can also adjust the bearing of the planes. Select the basic direction of northwest, northeast, southwest, or southeast for each plane, and then give the angle from north or south. The relationship among the distances from each plane to the origin and to each other are given by the Law of Cosines. The steps for working out the related rate and the final solution are given on the left. A scale drawing of the position of the planes at the time of interest is given on the right. Note that a, b, and c are all changing as time changes.