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CBSE Class 10 Answered

At a point A, 20 metres 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
Asked by Ayan2003dey | 26 Feb, 2019, 10:45: AM
answered-by-expert Expert Answer
Figure shows the angle of elevation and angle of depression of cloud seen from location A which is 20 m above ground level.
 
If the vertical height of cloud from level of A is H, then the reflection is seen from A at a depth of H+20 from ground level in the lake.
 
we have,  tan 30 = H/AD = 1/√3   or   AD = H√3  ............................(1)
 
we have , tan60 = FD/AD  = (H+40)/AD = √3   or H+40 = AD√3  = 3H  .......................(2)
[ we used AD = H√3 in above eqn.(2) using eqn.(1) ]
 
since,  H+40 = 3H,  we have  H = 20 m
 
Distance of cloud from A = AC = 2H = 40 m
Answered by Thiyagarajan K | 26 Feb, 2019, 11:59: AM

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