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.
Let AB be the surface of the lake and P be the point of observation such that AP = 20 metres. Let C be the position of the cloud and C’ be its reflection in the lake.
Then CB = C’B. Let PM be perpendicular from P on CB.
Then m∠CPM=30º and m∠C'PM=60°
Let CM = h. Then CB = h + 20 and C’B = h + 20.
In ΔCMP we have,
In ΔPMC' we have,
From equation (i) and (ii), we get
Now,CB=CM + MB =h +20= 20+ 20 = 40.
Hence, the height of the cloud from the
surface of the lake is 40 metres.