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 45° and from the same point the angle of
elevation of the top of the pedestal is 30°. Find the height of the pedestal.

Answer 1

Answer:

0.8(√3 + 1)m.

Step-by-step explanation:

Let the height of the pedestal be BC, the height of the statue, which stands on the top of the pedestal, be AB. D is the point on the ground from where the angles of elevation of the bottom B and the top A of the statue AB are 45° and 60° respectively.

The distance of the point of observation D from the base of the pedestal is CD. Combined height of the pedestal and statue AC = AB + BC

Trigonometric ratio involving sides AC, BC, CD, and ∠D (45° and 60°) is tan θ.

In ΔBCD,

tan 45° = BC/CD

1 = BC/CD

Thus, BC = CD

In ΔACD,

tan 60° = AC/CD

tan 60° = (AB + BC)/CD

√3 = (1.6 + BC)/BC [Since BC = CD]

√3 BC = 1.6 + BC

√3 BC - BC = 1.6

BC (√3 - 1) = 1.6

BC = 1.6 × (√3 + 1)/(√3 - 1)(√3 + 1)

= 1.6 (√3 + 1)/(3 - 1)

= 1.6 (√3 + 1)/2

= 0.8 (√3 + 1)

Height of pedestal BC = 0.8 (√3 + 1) m.