Question

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

The height of the chimney is 120m

Explanation:

Given that the angle of elevation of the top of a chimney from the top of a tower is 60° and the angle of depression of the foot of the chimney from the top of the tower is 30°.

The height of the tower is 40 m

We need to find the height of the chimney.

Let PQ be the chimney

Let AB be the tower where AB = 40 m

Also, given that $\angle A P B=30^{\circ}$ and $\angle P A Q=60^{\circ}$

Let us consider the triangle ABP

Thus, we have,

$\tan 30^{\circ}=\frac{A B}{A P}$

      $\frac{1}{\sqrt{3}}=\frac{40}{A P}$

     $A P=40 \sqrt{3} m$

Now, we shall consider the triangle APQ

Hence, we have,

$\tan 60^{\circ}=\frac{P Q}{A P}$

     $\sqrt{3}=\frac{P Q}{40 \sqrt{3}}$

     $120=PQ$

Thus, the height of the chimney is 120 m

Since, the minimum height of a smoke emitting chimney should be 100 m and the height of the chimney is 120 m.

Thus, the height of the chimney meets the pollution norms.

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Answer 2

Given : the angle of elevation of the top of a chimney from the top of a tower is 60 degree and the angle of depression of the foot of the chimney from the top of the tower is 30 degree. if the height of the tower is 40m

To find : height of the chimney

Solution :

Tower height = 40 m

Let say chimney Height = H m

Chimney height above tower = H - 40 m

Horizontal Distance between tower & chimney = D m

angle of elevation of the top of a chimney from the top of a tower is 60°

=> Tan 60 = (H - 40)/ D

=> √3 = (H - 40)/ D

=> D√3 = H - 40

angle of depression of the foot of the chimney from the top of the tower is 30°

=> Tan 30 = 40/D

=> 1/√3 = 40/D

=> D = 40√3

=> D√3 = 120

H - 40 = 120

=> H = 160

Chimney height = 160 m

120 m above tower height

Meetings the pollution Norms

Meetings the pollution NormsHence obeying the law & environment friendly