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Question

At a point A, 20 m above the level of water in a lake, the angle of elevation of a cloud is 30. The angle of elevation of the reflection of the cloud in the lake, at A is 60. Find the distance of the cloud from A.

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Solution

Let PQ be the surface of the lake. A is the point vertically above P such that AP=20 m.

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

Let BC=H meters

CQ= H + 20 and BD = H + 40

Now, In ABD

tan 60=BDAB

3=H+20+20AB

3.AB=H+40

AB=H+403 ...(i)

And, In ABC

tan 30=BCAB

13=BCAB

AB=3H....(ii)

From eq.(i) and (ii)

H+403=3H

3H=H+40

2H=40H=20

Putting the value of H in eq.(ii) ,we get

AB=203

Again,in ABC

(AC)2=(AB)2+(BC)2

=(203)2+(20)2

=1200+400

=1600

AC=1600 = 40 m

Hence,the distance of cloud from A is 40 m.


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