Question

A surveyor standing 63 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 48°. how tall is the radio tower?

Answer 1

The height of the radio tower is 20.77 meters.

If you draw a picture of the problem, you will see that you have to solve two right triangle problems with the tangent ratio.

If we subtract the measurements of the two triangles, we will have only the length of the radio tower.

tan(48) = x / 63
x = 69.97

tan(38) = x / 63
x = 49.22

69.97 - 49.22 = 20.77 for the height of the radio tower