ANGLE OF ELEVATION

Question

A balloon rises at a rate of 4 meters per second from a point on the ground 50 meters from an observer.Find the rate of change of the angle of elevation of the balloon from the observer when the balloon is 50 meters above the ground.

please show all solutions thanks

Answer 1

tan A = h/50
sec^2 A * dA/dt = (1/50) dh/dt

dA/dt = (4/50)cos^2 A

at h = 50, cos A = .707 and cos^2 A = 1/2

dA/dt = 4/100

Answer 2

thanks =)

Answer 3

How can you do this using cosign instead of tangent. I can't seem to get a answer.