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

The above diagram represents the problem in which C is the position of the cloud and D is the position of cloud's shadow.

Let AB = x

Let BC = h

As cloud is at a height of (20 + h) m from the water level. Its shadow will be (20 + h)m deep in the water.

So we have

BD = 20 + (20 + h) = (40 + h) mimpl

Now in ABC

In ABD

3h = h + 40

h = 20 m

Distance of point A from Cloud C = AC

By phythagoras theorm in triangle ABC

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

Implies AC = 40 m

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