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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.

Solution:

Let AB be the length of the statue and BC be the length of the pedestal.
In △BCD, BC/CD = tan 45°
∴ BC = CD
In △ACD, tan 60° = AC/CD
AB + BC/CD = √3
BC + 1.6 = √3 BC
BC + 1.6 = √3 BC
BC = 1.6/(√3 - 1);
BC = 1.6(√3 + 1)/(√3 - 1)(√3 + 1)
= 1.6(√3 + 1)/(3 - 1)
= 1.6(√3 + 1)/2
= 0.8(√3 + 1)m