# Trigonometry Word Problems: The Rate of Change of an Angle

Please see the attached file for the diagram associated with this problem.

Question: An airplane is flying at an altitude of 8 miles towards a point directly over an observer. If the speed of the plane is 615 miles per hour, find the rate at which the angle of observation, theta, changing by at the moment when the angle is 21 degrees.

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

find x when the angle is 21 degrees: tan Ñ² = opposite/adjacent = 0.384 = 8/x

x = 20.84 miles between where the plane is at time 0 and its got to travel 20.84 to be directly above the observer - that will take 615/20.84 = 29.51, 1/29.51 = 0.034 hours or 2.03 minutes. The angle between the initial viewing and when its directly above observer is 90-21 = 69o

69/2.03 = the angle is closing at 34 degrees per minute or 0.56 degrees per second

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