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A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 600; when he retires 20 m from the bank, he finds the angle to be 300. Find the height of the tree and the breadth of the river.

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sir this is the question from the book -ML aggarwal( avichal publication) class 10th , chapter20 , heights and distances
this question once has been asked in exam . and have chances to come in  future .
we know A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 600;
when he retires 20 m from the bank,
he finds the angle to be 300.
wehave to Find the height of the tree and the breadth of the river.
question no 17 , heights and distances , ICSE board

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1 Answer

  1. Consider TR as the tree and PR as the width of the river.

    ML Aggarwal Solutions for Class 10 Chapter 20 Image 17

    Take TR = X and PR = y

    In right triangle TPR

    tan θ = TR/PR

    Substituting the values

    tan 600 = x/y

    So we get

    √3 = x/y

    x = y √3…… (1)

    In right triangle TQR

    tan 300 = TR/QR

    tan 300 = x/(y + 20)

    We get

    1/√3 = x/(y + 20)

    x = (y + 20)/ √3 ….. (2)

    Using both the equations

    y√3 = (y + 20)/ √3

    So we get

    3y = y + 20

    3y – y = 20

    2y = 20

    y = 10

    Now substituting the value of y in equation (1)

    x = 10 × √3 = 10 (1.732) = 17.32

    Hence, the height of the tree is 17.32 m and the width of the river is 10 m.

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