Question

A surveyor standing 62 meters from the base of a building measures the angle to the top of the building and finds it to be 38°. The surveyor then measures the angle to the top of the radio tower on the building and finds that it is 45°. How tall is the tadio tower?

Answer 1

"How tall is the tadio tower?" is not clear. Do you mean its HEIGHT (how far its top is from the ground) or its VERTICAL LENGTH? Introducing the 38° angle to the top of the building implies the latter, but this could be a red herring.

Answer 2

clearly he means the height of the tower part of the setup.

The height h of the tower is found by noting that

h = 62tan45° - 62tan38°

Just draw a diagram and recall your basic trig functions.