Question

The angle of elevation of the top of a chimney from the top of a tower is 60º and the 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? [CBSE 2014]

Answer 1

Let AB be the tower and CD be the chimney.

Height of the tower, AB = 40 m
Suppose the height of the chimney be h m.
Draw AE ⊥ CD.
Here, CE = AB = 40 m
DE = CD − CE = (h − 40) m
In right ∆AEC,
$\tan 30°=\frac{CE}{AE}\Rightarrow \frac{1}{\sqrt{3}}=\frac{40}{AE}\Rightarrow AE=\frac{40}{\sqrt{3}}m$
In right ∆AED,
$\tan 60°=\frac{DE}{AE}\Rightarrow \sqrt{3}=\frac{h-40}{40\sqrt{3}}\Rightarrow h-40=120\Rightarrow h=120+40=160m$
Thus, the height of the chimney is $160$ m.
Clearly, the height of the chimney meets the pollution norms.
We should follow the pollution control norms and contribute to the cleaniness of the environment.