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Deepak Bora
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Height and distances : On the same side of a tower, two objects are located. When observed from the top of the tower, their angles of depression are 45º and 60º. If the height of the tower is 150 m, find the distance between the objects.

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On the same side of a tower, two objects are located. When observed from the top of the tower, their angles of depression are 45º and 60º. If the height of the tower is 150 m, fine the distance between the objects.

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  1. In triangle ABC, using tangent ratio,

    tanθ = AB/CB

    tan 60º = 150/x

    √3 = 150/x

    ∴ x = 150/√3

    x = 50√3m ( after rationalising)

    Similarly in triangle ABD,using tangent ratio

    tan θ = AB/DB

    tan 45º = 150/y

    1= 150/y

    ∴ y= 150m

    ∴ distance between the objects

    y-x = 150 – 50√3

    = 50(3-√3)

    = 50(3-1.732)

    = 63.4 m

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