I need help on this calculus problem, i explained the problem below?

Question

An airplane flies at an altitude of 5miles toward a point directly over an observer. The speed of the plane is 600mph. Find the rate at which the angle of elevation "theta" is changing when the angle is a) theta = 30degrees
b) theta = 60deg
c) theta = 75deg

Answer 1

The observer, the point 5 miles directly over the observer, and the location of the plane form a right triangle.

Theta is the interior angle at the vertex that is the plane.

tan(theta) = altitude/distance

Since we know the altitude, this lets us compute the distance for each of the values of theta that are of interest.

Also theta = arctan(altitude/distance) so the rate of change of theta with respect to time is the derivative:

d(theta)/dt = d(arctan(altitude/distance(t)))/dt

Applying the chain rule, etc. lets you calculate this for the desired values of theta.