Question

The angle of elevation of the top of a chimney form the foot 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 meters. Find the height of the chimney.

The angle of elevation of the top of a chimney from the foot 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 1

Let PQ be the chimney and AB be the tower.
We have,
AB = 40m,∠APB = 30°  and ∠PAQ = 60°
In ΔABP,

`tan 30° = (AB)/(AP)`

`⇒ 1/ sqrt(3) = 40/ (AP)`

`⇒ AP = 40 sqrt(3 ) m`

Now, in Δ APQ , 

` tan 60° = (OQ)/(AP)`

`⇒  sqrt(3) = (PQ) / (40 sqrt(3))`

∴ PQ = 120 m

So, the height of the chimney is 120 m.
Hence, the height of the chimney meets the pollution norms.
In this question, management of air pollution has been shown