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Home » The angle of elevation of the top of a chimney form the foot of a tower is and the angle of depression of the foot of the chimney from the top of the tower is . If the height of the tower is 40 meters. Find the height of the chimney.
The angle of elevation of the top of a chimney form the foot 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 40 meters. Find the height of the chimney.
CBSE | Class 10 | Maths | RS Aggarwal | Some Applications Of Trigonometry
The angle of elevation of the top of a chimney form the foot 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 40 meters. Find the height of the chimney.

Let \mathrm{PQ} be the chimney and \mathrm{AB} be the tower.

\mathrm{AB}=40 \mathrm{~m}, \angle \mathrm{APB}=30^{\circ} and \angle \mathrm{PAQ}=60^{\circ}

In \triangle \mathrm{ABP},

\tan 30^{\circ}=\frac{\mathrm{AB}}{\mathrm{AP}}

\Rightarrow \frac{1}{\sqrt{3}}=\frac{40}{\mathrm{AP}}

\Rightarrow \mathrm{AP}=40 \sqrt{3} \mathrm{~m}

=> in \triangle \mathrm{APO}.

\tan 60^{\circ}=\frac{\mathrm{PQ}}{\mathrm{AP}}

\Rightarrow \sqrt{3}=\frac{\mathrm{PQ}}{40 \sqrt{3}}

\therefore \mathrm{PQ}=120 \mathrm{~m}

=> the height of the chimney is 120 \mathrm{~m}.

=> the height of the chimney meets the pollution norms.

 

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