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?
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.