Find the height of the cloud cover

Question

To measure the height of the cloud cover at an airport, a worker shines a spotlight upward at an angle θ degrees from the horizontal. An observer 600 m away measures the angle of elevation to the spot of the light to be 45 degrees. Find the height h (in terms of θ degrees) of the cloud cover.

Answer 1

Check out the below video solution I provided. Hope it helps!

Answer 2

Draw label a diagram

tan 45° = h / x

x tan 45° = h

x = h / (tan 45°)

tan θ = h / (600 - x)

600 tan θ - x tan θ = h

-x tan θ = h - (600 tan θ)

x = [h - (600 tan θ)] / (-tan θ]

h / (tan 45°) = [h - (600 tan θ)] / (-tan θ]

Can you solve for h and answer?