What is the rate of change of the angle.?

Question

A Rocket is tracked by a radar station 6 miles away. When the rocket is 4 miles high its velocity is .5 miles/second. What is the rate of change of the angle.

Answer 1

Theta = arctan(4/6)
Assuming a flat earth, dtheta/dy = cos(theta)/r(hor), so dtheta/dt = (dtheta/dy)*(dy/dt) = cos(theta) * 0.5/6