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 the water.
Solution
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 =
Draw PM⊥CB
Let CM = h
∴ CB = h + 60 m
In ∆CPM
⇒ 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.
