He 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° Find the Height of the Chimney. - Mathematics

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.

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

Solution

Let PQ be the chimney and AB be the tower.
We have,
AB = 40m,∠APB = 30°  and ∠PAQ = 60°
In ΔABP,

tan 30° = (AB)/(AP)

⇒ 1/ sqrt(3) = 40/ (AP)

⇒ AP = 40 sqrt(3 ) m

Now, in Δ APQ ,

 tan 60° = (OQ)/(AP)

⇒  sqrt(3) = (PQ) / (40 sqrt(3))

∴ PQ = 120 m

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

Concept: Heights and Distances
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Chapter 14: Height and Distance - Exercises

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RS Aggarwal Secondary School Class 10 Maths
Chapter 14 Height and Distance
Exercises | Q 18

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