Question

Paul stands on the roof of a building that he knows is about 1100 ft. tall. He wants to estimate

the height of a neighboring building. He measures the angles of depression to the top of the

neighboring building and to the bottom of the neighboring building. He finds these angles to be

28° and 65°, respectively. How tall is the neighboring building?

Answer 1

The height of the neighboring building is 827.26 ft.

Explanation:

See the diagram attached.

Now, AB = 1100 ft and CE = h (say) and AC = b (say).

Now, from the right triangle Δ BDE,

`\tan 28^(\circ) = (DB)/(DE) = (1100 - h)/(b)` .............. (1)

Again, from the right triangle Δ ABC,

`\tan 65^(\circ) = (AB)/(AC) = (1100)/(b)`

⇒ b = 512.94 ft.

Now, from equation (1) we can say

`\tan 28^(\circ) = (1100 - h)/(512.94)`

⇒ h = 827.26 ft.

Therefore, the height of the neighboring building is 827.26 ft. (Answer)