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Deepak Bora
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Trigonometry hight and distance : ncert math class 10th chapter 9 question 2

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A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.

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  1. This answer was edited.

    In right ΔABD,

    Using Cosine ratio,

    cos 30° = AD/BD

    We know that, cos 30° = √3/2

    √3/2 = 8/BD

    ∴AC = 16/√3 …(1)

    using tangent ratio,

    tan 30° = AB/AD

    1/√3 = AB/8

    AB = 8/√3 ….(2)

    Total height of the tree is the sum of AB and BC,

    Therefore, total height of the tree = AB + BC

    16/3+ 8/√3 = 24/√3 = 8√3 m.

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