Question

The angle of elevation of a cloud from a point 60 m above the surface of the water of a lake is 30° and the angle of depression of its shadow in water of lake is 60°. Find the height of the cloud from the surface of water

Answer 1

Let AB be the surface of the lake and P be the point of observation such that AP = 60 m. Let C be the position of the cloud and C be its reflection in the lake

Then CB = C'B

Draw PM⊥CB

Let CM = h

∴ CB = h + 60 m

From equations (1) and (2):

`sqrt3h = (h + 120m)/sqrt3`

⇒ 3h = h + 120 m

⇒ 2h = 120 m

⇒ h = 60 m

CB = h + 60m = 60m + 60m = 120m

Thus, the height of the cloud from the surface of the lake is 120 m