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

Answer 1

\(AB = 40 m\)

\(\angle PAD = 30°\)

\(\therefore \angle BAD = 90° - 30° = 60°\)

In \(\triangle ABD,\)

\(\tan 60° = \frac{BD}{AB}\)

⇒ \(\sqrt 3 = \frac{BD}{40}\)

⇒ \(BD = 40\sqrt3\)

In \(\triangle BCD,\)

\(\tan 60° = \frac{CD}{BD}\)

⇒ \(\sqrt 3 = \frac{CD}{40\sqrt 3}\)

⇒ \(CD = (40\sqrt 3). \sqrt 3\)

⇒ \(CD = 40\times 3 = 120\)

\(\therefore \) Height of chimney = 120 m.

Answer 2

Let PQ be the chimney and AB be the tower. 

We have,

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