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Question
An observer 1.5m tall is 30 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.
Solution
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).
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