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    Question

    The distance between two pillars is 80 metres. The

    height of one pillar is twice of the other pillar. The angles of elevation of their top from the midpoint of the line connecting their feet are complementary to each other. The height of the big pillar is
    A 20√2 m Correct Answer Incorrect Answer
    B 20 m Correct Answer Incorrect Answer
    C 40√2 m Correct Answer Incorrect Answer
    D 40 m Correct Answer Incorrect Answer

    Solution

    In ∆ABP, tan θ = x/40 ……………. (i) In ∆ BCQ, tan (90 – θ) = 2x/40 Cot θ = 2x/40 ………. (ii) Multiplying both the equations, Tan θ. cot θ = x/40 × 2x/40 1 = x²/800 x² = 800 x = 20√2 Height of the big pillar = 2 × 20√2 = 40√2 m

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