A statue, 1.6 m tall, stands on the top of a pedestal. Find the height of the pedestal.

Question

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.

Answer 1

Let AB be the height of statue.
D is the point on the ground from where the elevation is taken.

Height of pedestal = BC = AC - AB

A/q,
In  right ΔBCD,
tan 45° = BC/CD
⇒ 1 =  BC/CD
⇒ BC = CD.
also,

In  right ΔACD,

tan 60° = AC/CD
⇒ √3 = AB+BC/CD

⇒ √3CD = 1.6 m + BC
⇒ √3BC = 1.6 m + BC
⇒ √3BC - BC = 1.6 m
⇒ BC(√3-1) = 1.6 m
⇒ BC = 1.6/(√3-1) m
⇒ BC = 0.8(√3+1) m
Thus, the height of the pedestal is 0.8(√3+1) m.