Question

A statue of height 6m stands on the top of a pedestal from a point on the ground the angle of elevation of the top of the status is60 degree and the same point the angle of elevation of the top of the pedestal is 30 degree find the height of the pedestal

Answer 1

Step-by-step explanation:

let AB be the statue of height 6 m tall standing on the top of pedestal BC and

let the height of pedestal be x i.e,BC

in triangle ACD

tan60=p/b

root 3=AC/CD

root3= 6+x/root3 -------1

again,

In triangle BCD

Tan 30=p/b

1/root3=BC/CD

CD=XROOT3

now putting this value of CD in eqn 1 we get,

CD=6+x/root3

xroot3=6+x/root3

root3*2x=6+x

3x=6+x

or, 3x-x= 6

or,2x=6

or, x=3

.

. . height of pedestal=3 m

Answer 2

Answer: Height of Pedestial is 3m

Step-by-step explanation:

Let the distance between point and pedestial be B and height of pedestial be x

Using Trigonometry

Tan 30 = x/B

B = (root3)x, (tan 30 = 1/(root3))

Tan 60 = x+6/B

B = x + 6/(root3), (tan 60 = (root3))

So,

(root3) x = x + 6/(root3)

Solving this equation

x = x + 6/3

3x = x + 6

x = 6/2

x = 3

So, x = 3

Height of Pedestial = 3m