From a point 20 m above the surface of a lake, the angle of elevation of a cloud is 30° and the angle of depression of the cloud's reflection in the lake is 60°. The height of the cloud above the lake surface is:

Let the cloud be H m above the lake and d m away horizontally. The elevation gives (H − 20)/d = tan30°, and because the reflection sits H m below the surface the depression gives (H + 20)/d = tan60°. Dividing the second equation by the first: (H + 20)/(H − 20) = √3 ÷ (1/√3) = 3, so 3H − 60 = H + 20 and H = 40 m. The value 60 m is the drop from the eye down to the reflection, 80 m is 2H, and 20√3 ≈ 34.6 m is the horizontal distance.