There are two, men and a tower in between. The distance between the men is 100 m. The angle of elevation to the top of the tower are 30° and 60° respectively. Find the height of tower.
Explanation:
Given, AB = 100. Let AD = x, hence, BD = 100 – x.
In ∆ACD, tan60° = √3 =CD/AD
⇒ CD = √3 × AD …(1)
In ∆BCD, tan30° = 1/√3 = CD/BD.
⇒ CD = BD/√3 …(2)
From (1) and (2)
⇒ √3 × AD = BD/√3
⇒ 3x = 100 – x
⇒ x = 25.
∴ CD = √3 × AD = 25√3.
Hence, option (b).
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