an airplane is flying at an altitude of 6.7 miles towards a point directly over an observer. if the speed of the plane is 499 miles per hour, find the rate at which the angle of observation, Ɵ, changing by at the moment when the angle is 21 degrees.

Answer 1

As usual, draw a diagram. If the plane is x miles away horizontally,

x/6.7 = tan Ɵ

dx/6.7 = sec^2 Ɵ dƟ

-499/6.7 = sec^2(21°) dƟ

dƟ = -65°/hr