feet per second help

Question

A rotating light is located 11 feet from a wall. The light completes one rotation every 4 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 20 degrees from perpendicular to the wall.

Answer 1

Draw a diagram of a light 11 feet from a wall (perpendicular to wall). Then draw a line from the light to the wall at some angle θ to the perpendicular line. Using trig the distance from the light to the wall at an angle θ is given by

D = 11/cosθ. The rate of change of the angle as the light rotates is dθ/dt which is 360º/4sec = 90º /sec.

Differentiating, dD/dt = 11 d(1/cosθ)/dt = 11 x - 1/cos²θ x -sin θ x dθ/dt = 11 x 1/cos²20º x sin20º x 90º/sec

Evaluating the trig functions and calculating, dD/dt = 383 ft/sec

Check my math.