Question

The angle of elevation of the top of a chimney from the top of a tower is ${60}^{\circ }$ and the angle of depression of the foot of the chimney from the top of the tower is ${30}^{\circ }$. If the height of the tower is $40m$, find the height of the chimney. According to pollution control norms, the minimum height of a smoke emitting chimney should be $100m$. State if the height of the above mentioned chimney meets the polution norms. What valued is discussed in this question?

Answer 1

Let $AB$ and $CD$ be a tower and chimney respectively. And, the height of the tower $=60m$

Let the height of building $=hm$

In triangle $APC$,

$tan{60}^{\circ }=\frac{PC}{AP}$

$\sqrt{3}=\frac{h-40}{x}$

$x=\frac{h-40}{\sqrt{3}}m$ -----(1)

In triangle ABD,

$tan{30}^{\circ }=\frac{AB}{BD}$

$\frac{1}{\sqrt{3}}=\frac{40}{x}$

$x=40\sqrt{3}$ -----(2)

From (1) & (2),

$\frac{h-40}{\sqrt{3}}=40\sqrt{3}$

$h-40=120$

$h=120+40$

$h=160m$

Hence, the height of the chimney is $160m$.

Hence, the height of chimney follow pollution control norms.