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A statue, 1.6 m 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°

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A statue, 1.6 m 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.

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Let AB be the height of statue.

D is the point on the ground from where the elevation is taken.

To Find: Height of pedestal = BC = AC - AB

From figure,

In right triangle BCD,

tan 45° = BC/CD

1 = BC/CD

BC = CD …..(1)

In right ΔACD,

tan 60° = AC/AD

√3 = (AB+BC)/CD

√3CD = 1.6 + BC

√3BC = 1.6 + BC (using equation (1)

√3BC – BC = 1.6

BC(√3-1) = 1.6

BC = 1.6/(√3-1) m

BC = 0.8(√3+1)

Thus, the height of the pedestal is 0.8(√3+1) m.

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