Question

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 60º and from the same point, the angle of elevation of the top of the pedestal is 45º. Find the height of the statue.

Answer 1

Answer:

2(√3 -1)

Step-by-step explanation:

Length of the pedestal = 2m (Given)

Angle of elevation of the top of the statue = 60º (Given)

Angle of elevation of the top of the pedestal is 45º (Given)

Let the statue = AB

The pedestal = BC

Point of observation = D

Tan45 = 2/d

Thus, d = 2

Tan60 = 2+h/d

√3 = 2+h/2

2√3 = 2+ h

2√3 -2 = h

h = 2 (√3 -1)

Therefore, the height of the statue is = 2 (√3 -1).