Q13 of 22 Page 9

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.(CBSE 2015)


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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