I don’t understand how to do this

Question

A rotating light is located 14 feet from a wall. The light completes one rotation every 2 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 15 degrees from perpendicular to the wall.

Answer 1

x = 14tanθ; dx/dt = 14sec²θdθ/dt = 14sec²15°·2π/2 = 47.14 feet/s

Answer 2

Draw a diagram of the beam at some position and hitting the wall. Distance,d, to wall is 14 feet. The position of the beam is at some angle θ = 15 degrees. The rate of change, dθ/dt = 2π rad/2 seconds or π rad/sec.

The equation for the x position along the wall comes from x/d = tanθ or x = dtanθ

Differentiating, dx/dt = d*sec²θ * dθ/dt at θ= 15 degrees