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From two points A and B on the same side of a building, the angles of elevation of the top of the building are 30 and 60 respectively. If the height of the building is 10 m, find the distance between A and B correct to two decimal places.

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sir this is the important  question from the book -ML aggarwal( avichal publication) class 10th , chapter20 , heights and distances
it is given that From two points A and B on the same side of a building,
the angles of elevation of the top of the building are 30 and 60 respectively.
If the height of the building is 10 m,
find the distance between A and B correct to two decimal places.

question no 28 , heights and distances , ICSE board

 

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1 Answer

  1. In triangle DBC

    tan 600 = 10/BC

    Substituting the values

    √3 = 10/BC

    BC = 10/√3

    In triangle DBC

    tan 300 = 10/ (BC + AB)

    Substituting the values

    1/√3 = 10/[10/√3 + AB]

    By further calculation

    1/√3 [10/√3 + AB] = 10

    So we get

    AB = 10√3 – 10/√3

    Taking LCM

    AB = (30 – 10)/ √3

    AB = 20/√3

    AB = 20√3/3

    So we get

    AB = (20 × 1.732)/ 3

    AB = 20 × 0.577

    AB = 11.540 m

    Hence, the distance between A and B is 11.54 m.

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