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From the second floor of a 100m tall building, the angle of depression of the bottom and top of another building exactly opposite to it is observed to be $60 ∘$ and $30 ∘$ respectively. What is the height of the building?

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66m

67m

66.67m

65m

answer is C.

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Detailed Solution

Let the diagram of the given situation be,
seo

Let h be the height of the other building. So,

E D = h

.
Since

B C = E D

, then

B C = h

.
We have,

A C = A B + B C 100 = A B + h A B = 100 − h

Δ A B E

, we have

tan 30 ∘ = A B B E B E = A B tan 30 ∘ = 100 − h 13 B E = 3 (100 − h)

Δ A C D

, we have

tan 60 ∘ = A C C D C D = 1003

Since

C D = B E

, then

(100 − h) 3 = 1003 100 − h = 1003 300 − 3 h = 100 h = 2003 h = 66.67 m

Hence, the correct option is 3.

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