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deepaksoni
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The angle of elevation of the top of an unfinished tower at a point distant 120 m from its base is 45. How much higher must the tower be raised so that its angle of elevation at the same point may be 60?

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sir this is the important  question from the book -ML aggarwal( avichal publication) class 10th , chapter20 , heights and distances
The angle of elevation of the top of an unfinished tower
at a point distant 120 m from its base is 45.
How much higher must the tower be raised
so that its angle of elevation at the same point may be 60?

question no 36 , heights and distances , ICSE board, ML Aggarwal

 

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1 Answer

  1. Consider AB as the unfinished tower where AB = 120 m

    Angle of elevation = 450

    Take x be higher raised so that the angle of elevation becomes 600

    BC = y

    ML Aggarwal Solutions for Class 10 Chapter 20 Image 38

    In right triangle ABC

    tan θ = AB/CB

    Substituting the values

    tan 450 = AB/CB = 120/y

    So we get

    1 = 120/y

    y = 120 m

    In right triangle DBC

    tan 600 = DB/CB

    Substituting the values

    √3 = (120 + x)/ 120

    120√3 = 120 + x

    x = 120√3 – 120

    x = 120 (√3 – 1)

    So we get

    x = 120 (1.732 – 1)

    x = 120 (0.732)

    x = 87.84 m

    Hence, the tower should be raised at 87.84 m.

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