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    Question

    A tree breaks due to storm and the broken part bends, so

    that the top of the tree touches the ground making an angle of 30┬░ with the ground. The distance between the foot of the tree to the point where the top touches the ground is 12 m. Find the height of the tree (in metres)
    A 36тИЪ3 m Correct Answer Incorrect Answer
    B 12тИЪ3 m Correct Answer Incorrect Answer
    C 12 m Correct Answer Incorrect Answer
    D 16тИЪ3 m Correct Answer Incorrect Answer

    Solution

    BC = 12 m Height of the tree = AB + AC Tan 30┬░ = AB/12 тЗТ (1/тИЪ3) = AB/12 тЗТ AB = (12/тИЪ3) Cos 30┬░ = BC/AC = 12/AC тЗТ ┬атИЪ3/2 = 12/AC тЗТ AC = 24/тИЪ3 Hence, AB + AC┬а= 12/тИЪ3 +┬а24/тИЪ3 = 36/тИЪ3 тЗТ 36/тИЪ3 ├Ч тИЪ3/тИЪ3 (rationalizing to remove root from denominator) тЗТ 36тИЪ3/3 = 12тИЪ3 тИ┤ Height of the tree = 12тИЪ3 m

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