Question

A statue which is x m tall stands on the top of 100m long pedestal on the ground. From a point on the ground, the angle of elevation of the top of the statue is 60 ^ 0 and from the same point, the angle of elevation of the top of the pedestal is 45 degrees . Find the height of the statue.​

Answer 1

Answer:

73 m

Step-by-step explanation:

tan 45° = 1

= (height of pedestal) / (distance of the point from

the base of pedestal)

-> height of pedestal = distance of the point = 100m

Now,

tan 60° = (total height) / (distance of the point)

root 2 = (x + 100) / 100

1.73 = (x + 100) / 100

1.73 × 100 = x + 100

on solving this,

x= 73 m

Answer 2

ANSWER:-

Height of the statue is 100(√3-1) metres

SOLUTION :-

Angle of Elevation of the top of the statue = 60°

Angle of Elevation of the top of Pedestal = 45°

Height of Pedestal =100m

The height of statue is x metres

Now , In ∆AOC ( Using Trigonometry ratios)

-

tan 60° = AC/BO

√3 BO = 100 + X

BO = 100+ X/√ 3 ------(I)

And , Again in ∆ BOC

tan 45° = BC/BO

1= 100/BO

BO = 100 -----(ii(

From equation (I) & ( ii) we get

100+/√ 3 = 100

100+ x = 100√ 3

x= 100√3 -100

x = 100(√3-1) m

Hence the height of the statue is 100(√3-1) metres .