An airplane flies at an altitude of 2 miles toward a point directly over an observer (see figure). The speed of the plane is 600 miles per hour. Find the rates at which the angle of elevation θ is changing when the angle is θ = 30°, θ = 60°, and θ = 70°.

Answer 1

I'll do θ = 30°
At that time, the horizontal distance is x, so

cotθ = x/2, so csc^2θ = 1+x^2/4 and x^2 = 12
-csc^2 θ dθ/dt = 1/2 dx/dt
-4 dθ/dt = 300
dθ/dt = -75 rad/hr