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Question

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.


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Solution

Let AB be the height of the statue.

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

To find the eight of pedestal =BC=AC-AB

From the figure AB =statue=1.6m

BC=pedestal=?

In ACD

PB=ACCD=tan60°

1.6+BCCD=3

3CD=1.6+BC

CD=1.6+BC3---------------{1}

In BCD,

BCCD=tan45°BCCD=1

CD=BC

From (1)

1.6+BC3=BC1

3BC=1.6+BC

1.732BC1BC=1.6

0.732BC=1.6

BC=1.60.732

BC=1610×100732=1600732

BC=2.18m

Hence, the height of the pedestal is2.18m.


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