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 60ϒ and from the same point the angle of elevation of the top of the pedestal is 40ϒ. Find the height of the pedestal. (tan 40° = 0.8391, `sqrt(3)` = 1.732)

#### Solution

Height of the statue = 1.6 m

Let the height of the pedestal be “h”

AD = H + 1.6 m

Let AB be x

In the right ∆ABD, tan 60° = `"AD"/"AB"`

`sqrt(3) = ("h" + 1.6)/x`

x = `("h" + 1.6)/sqrt(3)` ...(1)

In the right ∆ABC, tan 40° = `"AC"/"AB"`

0.8391 = `"h"/x`

x = `"h"/(0.8391)`

Substitute the value of x in (1)

`"h"/(0.8391) = ("h" + 1.6)/sqrt(3)`

(h + 1.6) 0.8391 = `sqrt(3)` h

0.8391 h + 1.34 = 1.732 h

1.34 = 1.732 h – 0.8391 h

1.34 = 0.89 h

h = `1.34/0.89`

= `134/89`

= 1.5 m

Height of the pedestal = 1.5 m