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 tower is 40 m, find the height of smoke emitting chimney. according to pollution control norms, the minimum height of a smoke emitting chimney should be 100 m.

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get 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 tower is 40 m, find the height of smoke emitting chimney. according to pollution control norms, the minimum height of a smoke emitting chimney should be 100 m. from screen.

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 polution norms. What valued is discussed in this 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 polution norms. What valued is discussed in this question?

Byju's Answer Standard X Mathematics Angle of Depression The angle of ... 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 polution norms. What valued is discussed in this question?

Open in App Solution

Let A B and C D

be a tower and chimney respectively. And, the height of the tower

= 60 m

Let the height of building

= h m In triangle A P C , t a n 60 ∘ = P C A P √ 3 = h − 40 x x = h − 40 √ 3 m -----(1) In triangle ABD, t a n 30 ∘ = A B B D 1 √ 3 = 40 x x = 40 √ 3 -----(2) From (1) & (2), h − 40 √ 3 = 40 √ 3 h − 40 = 120 h = 120 + 40 h = 160 m

Hence, the height of the chimney is

160 m .

Hence, the height of chimney follow pollution control norms.

Suggest Corrections 40

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?

Click here👆to get an answer to your question ✍️ 29 The angle of elevation of the top of a chimney from the foot of a tower is $ 60 ^ { \circ } $ and the angle of depress the of the foot of the chimney from the top of the tower is $ 30 ^ { \circ } . $ If the height of the tower is $ 40 \mathrm { m } , $ find the height of the chimney.

Question

29 The angle of elevation of the top of a chimney from the foot of a tower is 60

∘

and the angle of depress the of the foot of the chimney from the top of the tower is 30

∘

. If the height of the tower is 40m, find the height of the chimney.

Open in App

Updated on : 2022-09-05

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The angle of elevation of the top of a chimney from the top of the 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 the pollution control norms, the minimum height of a smoke emitting chimney should be 100 meters. State if the height of the above mentioned chimney meets the pollution norms.

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

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

60 ∘ 60∘

and the angle of depression of the foot of the chimney from the top of the tower is

30 ∘ 30∘

. If the height of the tower is 40m, find the height of the chimney. According to the pollution control norms, the minimum height of a smoke emitting chimney should be 100 meters. State if the height of the above mentioned chimney meets the pollution norms.

Last updated date: 12th Mar 2023

• Total views: 292.5k • Views today: 6.73k Answer Verified 292.5k+ views

Hint: Assume that the height of the cloud above the lake level is ‘h’. Draw a rough diagram of the given conditions and then use the formula

tanθ= perpendicular base

tan⁡θ=perpendicularbase

in the different right angle triangles and substitute the given values to get the height.

Complete step-by-step answer:

Let us start with the question by drawing a representative diagram of the situation given in the question.

According to the above figure:

AE is the chimney and BD is the tower. From the figure we can also see that BD is equal to ME.

We have assumed the height of the chimney as ‘h’. Therefore, AE = h meters. Also, assume that the distance BM is ‘y’ meters.

Now, in right angle triangle ABM,

∠ABM= 60 ∘ ∠ABM=60∘ We know that, tanθ= perpendicular base

tan⁡θ=perpendicularbase

. Therefore, tan 60 ∘ = AM BM tan⁡60∘=AMBM

Since, BD = ME = 40 m, because they are opposite sides of the rectangle BDEM. Therefore,

AM = AE – EM = h – 40.

⇒tan 60 ∘ = AM BM ⇒tan⁡60∘=AMBM ⇒tan 60 ∘ = h−40 y ⇒tan⁡60∘=h−40y ⇒y= h−40 tan 60 ∘

.......................(i)

⇒y=h−40tan⁡60∘.......................(i)

Now, in right angle triangle BME,

∠EBM= 30 ∘ ∠EBM=30∘ We know that, tanθ= perpendicular base

tan⁡θ=perpendicularbase

. Therefore, tan 30 ∘ = EM BM tan⁡30∘=EMBM ⇒tan 30 ∘ = 40 y ⇒tan⁡30∘=40y ⇒y= 40 tan30 ∘

.......................(ii)

⇒y=40tan⁡30∘.......................(ii)

From equations (i) and (ii), we get,

h−40 tan 60 ∘ = 40 tan 30 ∘

h−40tan⁡60∘=40tan⁡30∘

Substituting tan 30 ∘ = 1 3 – √ and tan45 ∘ = 3 – √

tan⁡30∘=13 and tan45∘=3

, we get, h−40 3 – √ = 3 – √ ×40 1 h−403=3×401

By cross multiplication, we get,

h−40=120 h−40=120 ⇒h=160 ⇒h=160

Therefore, the height of the chimney is 160 meters. Also, the height is greater than 100 m, so meets the pollution norms.

Note: One may get confused in removing the unknown variables. Therefore, remember that we have to find the value of variable ‘h’ and we have to remove all other variables. We have used the tangent of the given angle because we have to find the height and we have a common base in two right angle triangles that can be easily cancelled.

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