A man is standing at some distance from a building. There is a pole at the top of the building. The building subtends an angle of 30° at the man and the angle of elevation of the top of the pole is 45°. Find the height of the pole if the building is 50m high.
Explanation:
Given, BC = 50 m.
Let CD = x.
In ∆ ABC, tan45° = 1/√3 = BC/AB
⇒ AB = BC × √3 = 50√3.
In ∆ ABD, tan45° = 1 = BD/AB
⇒ BD = AB
⇒ 50 + x = 50√3
⇒ x = 50(√3 - 1)
Hence, option (a).
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