The angle of depretion from the top of a tall building to the top of a shorter building is 18 degrees and the angle of depretion from the taller building to the base of the shorter building is 32 degrees. The hight of the shorter building is 200 feet. What is the height of the taller building?

"depretion"? I guess I don't know that word.

Tan(α) = X/D
Tan(β) = (X+200)/D
X is the height of the higher tower above the height of the 200 ft tower.
D is the distance between the towers.

Tan(α)/Tan(β) = X/(X+200)
The factor, D, drops out. It doesn't matter what it is.

α = 18 deg
β = 32 deg

Calculate the ratio of the tangents and solve for X

They mean 'angle of depression'