From a distance of 1500 feet from the​ spotlight, the angle of elevation the θ equals 39°2′. Find the height of the cloud base.

Tan = opposite/adjacent 

tan (39- 2') =height/1500

1500 x tan 39-2') = height = 1216.12 ft

Found as follows:

tan (39 + 2/60) = h / 1500   rearrange

1500 tan (39 + 2/60)  = h  ≈ 1216.12   ft