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    Question

    A man observes the top of a tower at an angle of

    elevation of 45°. He walks 50 meters towards the tower, and the angle of elevation becomes 60°. What is the height of the tower?
    A 25(√3+3) meters Correct Answer Incorrect Answer
    B 50√3 meters Correct Answer Incorrect Answer
    C 25(√3-3) meters Correct Answer Incorrect Answer
    D 50(√3+3) meters Correct Answer Incorrect Answer

    Solution

    Let the height of the tower be h, and the initial distance from the man to the tower be d. From the first observation: tan(45°) = h/d, so h = d. From the second observation: tan(60°) = h/(d - 50), so h/(d - 50) = √3. Substitute h = d into the second equation and solve to get h = 25(√3+3) meters. Correct option: a) 25(√3+3) meters

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