A statue stands on the top of a 2m tall 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 statue
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CD = 2m
Let BC = x
In ABC
Tan45° BC AB
Tan45° AB
AB = x
In AABD
Tan60° BD AB
BD=AB √3=x√3
We know CD BD - BC = 2m
√3x - x = 2
⇒ x(√3 - 1) = 2
⇒ x = 2 ⇒ x = √3+1m, which is the height.
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