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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?

Respuesta :

Answer:

The height of the neighboring building is 827.26 ft.

Step-by-step explanation:

See the diagram attached.

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

Now, from the right triangle Δ BDE,

[tex]\tan 28^{\circ} = \frac{DB}{DE} = \frac{1100 - h}{b}[/tex] .............. (1)

Again, from the right triangle Δ ABC,

[tex]\tan 65^{\circ} = \frac{AB}{AC} = \frac{1100}{b}[/tex]

⇒ b = 512.94 ft.

Now, from equation (1) we can say

[tex]\tan 28^{\circ} = \frac{1100 - h}{512.94}[/tex]

⇒ h = 827.26 ft.

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

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