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The angle of elevation of the top of a tower from the bottom of a building is twice that from its top. What is the height of the building, if the height of the tower is 75 m and the angle of elevation of the top of the tower from the bottom of the building is 60°?

(a) 25 m

(b) 37.5 m

(c) 50 m

(d) 60 m

1 Answer

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Best answer

(C) 50 m

Let the height of the building AB be h metres and the distance between AB and tower EC be x metres. 

Given, ∠EAD = 30°, ∠EBC = 60°

In rt. Δ ADE,

tan 30° = \(\frac{ED}{AD}=\frac{75-h}{x}\)

⇒ \(\frac{1}{\sqrt3}= \frac{75-h}{x}\)

⇒  x = (75 - h)\(\sqrt3\) ...(i)

In rt. Δ EBC,

tan 60° = \(\frac{EC}{BC}\)

⇒ \(\sqrt3\) = \(\frac{75}{x}\)

⇒ \(x= \frac{75}{\sqrt3}\) ...(ii)

∴ From (i) and (ii),

\(\frac{75}{\sqrt3}\) = (75 – h)\(\sqrt3\)

⇒ 75 = (75 – h) × 3

⇒ 75 = 225 – 3h

⇒ 3h = 150

⇒ h = 50 m.

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