How tall is the tower?

Question

A radio tower is located 325 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  and that the angle of depression to the bottom of the tower is . How tall is the tower?

Answer 1

Draw an imaginary line from the window parallel to the ground under the tower. This will split the tower into the upper part x and the lower part y.

tan(34°) = opp/adj = x/325

x = 325 tan(34°) ≈ 219.2 feet

tan(31°) = y/325

y = 325 tan(31°) ≈ 195.28 feet

The total height of the tower = x+y = 414.48 feet.