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    Question

    The angle of elevation of the top of a building from the

    foot of a tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the height of the tower is 42 m, what is the height of the building? 
    A 42/√3 m Correct Answer Incorrect Answer
    B 14 m Correct Answer Incorrect Answer
    C 14√3 m Correct Answer Incorrect Answer
    D 42√3 m Correct Answer Incorrect Answer

    Solution

    Let AB and CD denote the tower and the building respectively. In △ABC, tan 60° = AB/BC ⇒ √3 = 42/BC ⇒ BC = 42/√3 m In △BCD, tan 30° = CD/BC ⇒ 1/√3 = CD/(42/√3) ⇒ CD = 14 m ⇒ h = 14 m

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