Question

A statue 1.46 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 60° and from the same point, the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal. [Use `sqrt(3) = 1.73`.]

Answer 1

Let AC be the pedestal and BC be the statue such that BC = 1.46m.
We have:

∠ADC = 45°  and ∠ADB = 60°
Let:
AC = hm and AD = xm

In the right ΔADC,we have:

`(AC)/(AD) = tan 45° = 1`
`⇒ h/x = 1`
⇒ h = x
Or,
x = h

Now, in the right ΔADB,we have:
`(AB)/(AD) = tan 60° = sqrt(3)`
`(h+1.46)/x = sqrt(3)`
On putting x  = h in the above equation, we get

`(h+1.46)/h = sqrt(3)`

`⇒ h +  1.46 = sqrt(3)h`

`⇒ h( sqrt(3)-1) = 1.46`

`⇒ h = 1.46/( sqrt(3)-1) = 1.46/0.73 = 2m`

Hence, the height of the pedestal is 2 m.