Question

The angle of elevation of the top of a chimney from the top of a tower is `60o` and t he angle of depression of the foot of the chimney from the top of the tower is `30o` . If the height of the tower is 40 m, find the height of the chimney. According to pollution control norms, the minimum height of a smoke emitting chimney should be 100 m. State if the height of the above mentioned chimney meets the pollution norms. What value is discussed in this question?

Answer 1

Correct Answer - `120 m`
Let `AB` be the tower and CD be the chimney.
From right `DeltaACD`, we have
`(AC)/(CD)= cot 60^(@) = 1/(sqrt(3)) rArr (AC)/(h) =1/(sqrt(3)) rArr AC = h/(sqrt(3)) "……"(i)`
From right `DeltaCAB`, we have
`(AC)/(AB) = cot 30^(@) = sqrt(3) rArr AC = 40sqrt(3)"..........."(ii)`.
From (i) and (ii), we get `h/(sqrt(3)) = 40sqrt(3) rArr h = 120`
Clearly, the height of the given chimney meets the pollution norms.
We should completely with the prescribed rules and contribute to the cleanlines enviroments.