Q. 714.2( 15 Votes )

The angle of elevation of the top of a chimney from the top of a tower is 60° and the angle of depression of the foot of the chimney from the top of the tower is 30°. 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 :

In the fig AB is the Chimney and CD is the tower of 40m


In ∆AED


tan 60° =


√3 =


h = √3DE ……………..(1)


In ∆DEB


tan 30° =


=


DE = 40√3 ………………..(2)


On substituting value of DE from


eqn (2) in eqn (2), we get


h = √3 × 40√3 = 120



Therefore height of Chimney is 40 + 120 = 160m


Yes, the height of the chimney meets the pollution norms.


Chimneys are made tall so that smoke should go high in the atmosphere in order to minimize air pollution.


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