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    Question

    Two buildings are collinear with the base of a tower and

    are at a distance 9m and 16m from the base of the tower. The angles of elevation from these two building of the top of the tower are complementary. What is the height of the tower?
    A 14m Correct Answer Incorrect Answer
    B 16m Correct Answer Incorrect Answer
    C 8m Correct Answer Incorrect Answer
    D 12m Correct Answer Incorrect Answer

    Solution

    Let the height of the tower be h And ∠CBD = θ and ∠ DAC = 90 – θ In ∆ BCD tan θ = CD/BC = h/9 …………(i) In ∆ ACD tan(90 - θ) = CD/AC cot θ = h/16 ……………………….(ii) On multiplying Equation (i) and (ii) tan θ × cot θ = h/9 × h/16 1 = h²/144 Now h = 12 m

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