Question

An observer 1.5 m tall is 30 m away from a chimney. The angle of elevation of the top of the chimney from his eye is 60°. Find the height of the chimney.

Answer 1

Let CE and AD be the heights of the observer and the chimney, respectively.
We have,
BD = CE = 1.5 m, BC = DE = 30 mand ∠ACB = 60°
In ΔABC

`tan 60° = (AB)/(BC)`

`⇒ sqrt(3 ) = (AD-BD)/30`

`⇒ AD -1.5 =30 sqrt(3)`

`⇒  AD = 30sqrt(3) +1.5`

`⇒  AD = 30XX 1.732 + 1.5`

`⇒  AD = 51.96 + 1.5`

`⇒  AD = 53.46 m`

So, the height of the chimney is 53.46 m (approx).