Question

A statue 1.6 m tall stands on top of a pedestal, from the point on th ground, the anlge of elevation of the top of the statue is 600 and from the same point, the angle of elevation of the top of the pedestal is 450. Find 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.

Hope it helps!

Answer 2

here is your answer my friend.