Question

A statue stands on the top of a 2 m 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.

Answer 1

Height of the pedestal = 2 m. 

Let the height of the statue = h m. 

Angle of elevation of top of the statue = 60°. 

Angle of elevation of top of the pedestal = 45°. 

Let the distance between the point of observation and foot of the pedestal = x m.

From the figure 

tan 45° = \(\frac{2}{x}\)

1 = \(\frac{2}{x}\)

∴ x = 2 m. 

Also tan 60° = \(\frac{2+h}{x}\)

⇒ √3 = \(\frac{2+h}{x}\)

⇒ 2√3 = 2 + h 

⇒ h = 2√3 – 2 

= 2(√3-1) 

= 2(1.732 – 1) 

= 2 × 0.732 

= 1.464 m.