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    Question

    From a point located x meters away from the base of a

    tree, the angle of elevation to the top of the tree is 60 ∘ . If the tree is 54 meters tall, determine the distance x from the point to the base of the tree.
    A 30 metres Correct Answer Incorrect Answer
    B 18√3 metres Correct Answer Incorrect Answer
    C 36√2 metres Correct Answer Incorrect Answer
    D 27√3 metres Correct Answer Incorrect Answer

    Solution

    In the given figure, let points 'A' and 'B' represent the top of the tree and the base of the tree, respectively and let 'C' represents the point on the ground that is 'x' metres away from the base of the tree (BC = x). In right triangle ABC tan 60o = (AB/x) Or, (54/x) = √3 So, x = 54 ÷ √3 = 18√3 metres

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