Calculus. Question

Question

A ladder 5 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1ft/sec, how fast. Is the angle between the ladder and the ground changing when the bottom of the ladder is 3ft from. The wall?

Answer 1

Let h(t) be the height on the wall of the top of the ladder

h(t) = 5 sin θ(t) and dh/dt = 5 cos θ dθ/dt

When the distance of the bottom of the ladder from the wall is 3 feet, cos θ = 3/5.

Therefore 1 = 5*(3/5)* dθ/dt and dθ/dt = 1/3 (radians per min)