Question

An airplane flies at an altitude of
y = 5
miles toward a point directly over an observer (see figure). The speed of the plane is 500 miles per hour. Find the rates at which the angle of elevation 𝜃 is changing when the angle is
𝜃 = 45°,

𝜃 = 60°,
and
𝜃 = 70°.

Answer 1

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Answer 2

when the plane is at a distance x miles from directly over the observer,
tanθ = 5/x
sec^2θ dθ/dt = -5/x^2 dx/dt
So, when θ=60°, 5/x = √3 and you have
4 dθ/dt = -3/5 * -500
dθ/dt = 75 rad/hr