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    Question

    A man standing on the top of a cliff observes a boat at

    an angle of depression of 45°. He then moves 30 meters further down the cliff, and the angle of depression of the boat is now 30°. How high is the cliff?
    A 15(3+√3) meters Correct Answer Incorrect Answer
    B 15(3-√3) meters Correct Answer Incorrect Answer
    C 15√3 meters Correct Answer Incorrect Answer
    D 15(1+√3) meters Correct Answer Incorrect Answer

    Solution

    Let the initial height of the cliff be h and the horizontal distance to the boat be d. From the first observation: tan(45°) = h/d, so h = d. From the second observation: tan(30°) = (h - 30)/d, so (h + 30)/d = 1/√3. Substituting h = d into the second equation: (h + 30)/h = 1/√3. Solving, we get h = 15(3+√3) meters. Correct option: a

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