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Deepak Bora
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A statue 1.6m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal. (Use √3 = 1.73 )

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CBSE 10th Class Mathematics
Past year question paper
Year 2020
SET 1, Code Number  – 30/5/1
Question Number –  39
trigonometric function
use trigonometric relation
sin, cos and tan relation

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  1. As per figure, BC = h m

    In right triangle ACP,

    tan 60° =  AC / PC

    √3 = [AB + BC] / PC

    √3 = [1.6 + h] / PC       …. (1)

    In right triangle BCP,

    tan 45° =  BC / PC

    1 = h / PC                      … (2)

    Dividing (1) by (2), we get

    √3 / 1 = [1.6 + h] / h

    h√3  = 1.6 + h

    h[√3 – 1] = 1.6

    h = 1.6 / [√3 – 1]

    h =  { ( 1.6 / [√3 + 1] ) / ( [√3 – 1] [√3 + 1] ) )

    h = 0.8 [√3 + 1]

    h=0.8(1.73+1)=0.8 x 2.73 =2.184 m

    Hence, the height of the pedestal is 2.184 m

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