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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?

User Lydell
by
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1 Answer

3 votes

Answer:

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)

Paul stands on the roof of a building that he knows is about 1100 ft. tall. He wants-example-1
User Stagleton
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