Question

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 metres, then find the height of the chimney.

According to pollution control norms, the minimum height of a smoke emitting chimney should be 100 metres. State if the height of the above mentioned chimney meets the pollution norms. What value is discussed in this question? [CBSE 2014]

Answer 1

Let PQ be the chimney and AB be the tower.

We have,

$$\begin{gathered} \mathrm{AB}=40\mathrm{m},\angle \mathrm{APB}=30°\mathrm{and}\angle \mathrm{PAQ}=60° \\ \mathrm{In}∆\mathrm{ABP}, \\ \tan 30°=\frac{\mathrm{AB}}{\mathrm{AP}} \\ \Rightarrow \frac{1}{\sqrt{3}}=\frac{40}{\mathrm{AP}} \\ \Rightarrow \mathrm{AP}=40\sqrt{3}\mathrm{m} \\ \mathrm{Now},\mathrm{in}∆\mathrm{APQ}, \\ \tan 60°=\frac{\mathrm{PQ}}{\mathrm{AP}} \\ \Rightarrow \sqrt{3}=\frac{\mathrm{PQ}}{40\sqrt{3}} \\ \therefore \mathrm{PQ}=120\mathrm{m} \end{gathered}$$

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.
a