The height of a tower is 50 ft and the height of a building is 20 ft.

Question

If the angle of depression from the top of the tower to the top of the building is 35.9°, what is the distance between the two, to the nearest foot?

?? feet

Answer 1

If you draw a picture of the building and tower

+--------------------------------

|\ 35.9° = θ

| \

30| θ \

+----+

| x |

20| | Building

+----+

x

From the picture and opposite angles of parallel lines are equal

tan(39.5°) = 30/x

x = 30/tan(39.5°) ≈ 36 feet

Answer 2

tan(35.9) = x/30 --> x = 22 ft