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An observer 1.5 m tall is 30 m away fro...

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.

Text Solution

Verified by Experts

The correct Answer is:
`53.46 m`
Let AB be the chimney and Cd be the observer.
Draw `DE_|_AB`.
Then, `AE = CD = 1.5 m`.
Let `AB = x` metres. Then, `BE = (x - 1.5) m`.
`angleEDB = 60^(@)`.
Also, `DE = CA = 30 m`
Also , `DE = CA = 30 m` .
From right `DeltaBED`, we have
`(BE)/(DE) = tan 60^(@)`.
`rArr (x - 15)/(30) = sqrt(3)`.
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