A radio tower is located 400 feet from a building. from a window in the building, a person determines that the angle of elevation to the top of the tower is 41 ∘ 41∘ and that the angle of depression to the bottom of the tower is 33 ∘ 33∘. how tall is the tower?

The solution is:

The height is computed by:

h (t) = h (1) + h (2)

h (1):

tan41 = h (1) / 400ft

h (1) = 400 (0.8693) = 347.72 ft

h (2):

tan33 = h (2) / 400 ft

h (2) = 400 (0.6494) = 259.76 ft

So combining the two:

h (t) = 347.72 + 259.76 = 607.48 feet

The tower is 607.48 feet tall.