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From the top of the tower of height 60m, the angle of depression of the top and the bottom of a building are observed to be $30 ∘$ and $60 ∘$ respectively. Find the height of the building.

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20m

60m

80m

40m

answer is D.

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Detailed Solution

Let the diagram of the situation be,
seo

In the triangle ABC, we have

∠ C = 60 ∘

and

A B = 60 m

. Then the length of the BC is,

tan C = A B B C tan 60 ∘ = 60 B C tan 60 ∘ = 3 B C = 603 m

In triangle ADE, we have

B C = 603 m

and

∠ D = 30 ∘

. Then, the length of the AE is,

tan D = A E E D tan 30 ∘ = A E 603 13 = A E 603 A E = 603 × 13 m A E = 20 m

Therefore,

C D = B E = A B − A E = 60 m − 20 m = 40 m

Hence, the correct option is 4.

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