# the angle of elevation of a cloud from a point 60 m above the surface of the water of a lake is 30° and the angle of depression of its shadow in water of lake is 60°. find the height of the cloud from the surface of water.

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## The angle of elevation of a cloud from a point 60 m/s above the surface of the water a lake is 30^o and the angle of depression of its shadow from the same point in water of lake is 60^o . Find the height of the cloud from the surface of water.

Click here👆to get an answer to your question ✍️ The angle of elevation of a cloud from a point 60 m/s above the surface of the water a lake is 30^o and the angle of depression of its shadow from the same point in water of lake is 60^o . Find the height of the cloud from the surface of water.

The angle of elevation of a cloud from a point 60 m/s above the surface of the water a lake is 30Question o

and the angle of depression of its shadow from the same point in water of lake is 60

o

. Find the height of the cloud from the surface of water.

Medium Open in App

Updated on : 2022-09-05

DC=H.Solution Verified by Toppr DB=D ′ B=(60+H) In △ECDtan30 0 = EC DC = EC H EC= 3 H In △ECDtan60 0 = EC D ′ C = EC D ′ B+BC = 3 H 60+H+60 3H=120+H H=60m

Height of cloud =60+60=120m.

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## The angle of elevation of a cloud from a point 60 m above a lake is 30∘ and the angle of depression of the reflection of cloud in the lake is 60∘. Find the height of the cloud. [4 MARKS]

The angle of elevation of a cloud from a point 60 m above a lake is 30∘ and the angle of depression of the reflection of cloud in the lake is 60∘. Find the height of the cloud. [4 MARKS]

Byju's Answer Standard IX Mathematics Angle of Depression The angle of ... Question

The angle of elevation of a cloud from a point 60 m above a lake is

30 ∘

and the angle of depression of the reflection of cloud in the lake is

60 ∘

. Find the height of the cloud.

Open in App Solution

Let AB be the surface of the lake and let P be a point vertically above A such that AP = 60 m

Let C be the position of the cloud and let D be its reflection in the lake.

Draw P Q ⊥ C D , Then, ∠ Q P C = 30 ∘ , ∠ Q P D = 60 ∘ , BQ = AP = 60 m Let C Q = x m e t r e s . Then, B D = B C = ( x + 60 ) m From right Δ P Q C , we have P Q C Q = cot 30 ∘ = √ 3 ⇒ P Q x = √ 3 ⇒ P Q = x √ 3 m -----------(i) From right Δ P Q D , we have P Q Q D = cot 60 ∘ = 1 √ 3 ⇒ P Q ( x + 60 + 60 ) m = 1 √ 3 ⇒ P Q = ( x + 120 ) √ 3 m -------(ii)

Equating the values of PQ from (i) and (ii), we get

x √ 3 = ( x + 120 ) √ 3 m ⇒ 3 x = x + 120 ⇒ 2 x = 120 ⇒ x = 60 ∴

height of the cloud from the surface of the lake

= B C = ( 60 + x ) m = ( 60 + 60 ) m = 120 m

Hence, the height of the cloud from the surface of the lake is 120 meters.

**Alernative Method**

In Δ A B E , we have tan 30 ∘ = h x ⇒ 1 √ 3 = h x ⇒ x = h √ 3 … … ( 1 ) In Δ B D E , we have tan 60 ∘ = 120 + h x ⇒ √ 3 = 120 + h h √ 3 ⇒ 3 h = 120 + h ⇒ 2 h = 120 ⇒ h = 60 m

Hence, height of cloud above the lake

= 60 + h = 60 + 60 = 120 m Suggest Corrections 112

SIMILAR QUESTIONS

**Q.**The angle of elevation of a cloud from a point 60 m above a lake is

30 ∘

and the angle of depression of the reflection of cloud in the lake is

60 ∘

. Find the height of the cloud. [4 MARKS]

**Q.**The angle of elevation of a cloud from a point

60 m above a lake is 30 ∘

and the angle of depression of the reflection of the cloud in the lake is

60 ∘

. Find the height of the cloud.

**Q.**

If the angle of elevation of a cloud from a point 60 m above a lake is 30 and the angle of depression of its reflection in the lake be 60 .find the height of the cloud from the surface of the lake.

**Q.**The angle of elevation of a cloud from a point

200

metres above a lake is

30 o

and the angle of depression of the reflection of the cloud in the lake is

60 o

. Find the height of the cloud.

**Q.**If the angle of elevation of a cloud from a point 100 m above a lake is 30° and the angle of depression of the reflection of the cloud in the lake from the same point is 60°, then the height of the cloud above the lake is

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Standard IX Mathematics

## The angle of elevation of a cloud from a point 60m\/s above the surface of the water a lake is 30 degree and the angle of depression of its shadow from the same point in the water of the lake is 60 degree. Find the height of the cloud from the surface of the water.

The angle of elevation of a cloud from a point 60m\/s above the surface of the water a lake is 30 degree and the angle of depression of its shadow from the same point in the water of the lake is 60 degree. Find the height of the cloud from the surfac...

## The angle of elevation of a cloud from a point 60m/s above the surface of the water a lake is 30 degree and the angle of depression of its shadow from the same point in the water of the lake is 60 degree. Find the height of the cloud from the surface of the water.

Last updated date: 15th Mar 2023

• Total views: 275.1k • Views today: 3.55k Answer Verified 275.1k+ views

**Hint:**In the given question first we will draw the diagram according to the given conditions in the question. Then according to the question, we will make equations for the given angle of elevation and angle of depression which are 30 degrees and 60 degrees respectively, and find the value of height. Thus we will get the right answer.

**Complete step by step solution:**Draw the diagram according to the question:

Now Let AO=H CD=OB= 60 60 m A’B=AB= 60+h 60+h ……………….. (1) (1) Now in triangle AOD tan 30 0 = AO OD = H OD H= OD 3 – √

tan300=AOOD=HODH=OD3

Because the value of

tan 30 0 = 1 3 – √ tan300=13 Thus OD= 3 – √ H OD=3H

Now in triangle A’OD

tan 60 0 = O A ′ OD = OB+B A ′ OD ⇒ 3 – √ = 60+60+H 3 – √ H = 120+H 3 – √ H

tan600=OA′OD=OB+BA′OD⇒3=60+60+H3H=120+H3H

Because the value of

tan 60 0 = 3 – √ tan600=3

And according to equation 1

We get A’B=AB= 60+h 60+h Now 120+H=3H ⇒120=2H ⇒H=60m

120+H=3H⇒120=2H⇒H=60m

Thus the height of the cloud from the surface of the water is60m 60m **.**

**Note:**First of all draw we have to draw a system diagram for the question according to the given instruction. The angle of elevation and angle of depression is given in the question. We have to remember the actual definition of Angle of elevation and angle of depression, so that diagrams and equations can be made properly. After making an equation for both Angle of elevation and angle of depression compare them and find the height of the cloud from the surface.

Guys, does anyone know the answer?