Question

The angle of elevation of a stationary cloud from a point 25m above a lake is 30° and the angle of depression of its reflection in the lake is 60°. What is the height of the cloud above the lake-level? 

Answer 1

Let C be the position of the cloud, l be the surface of the lake and D be the reflection of the cloud. 
Let CB = h, then OD = 25 + h 

In ΔABC,

`tan 30^circ = "BC"/"AB"`

⇒ `1/sqrt(3) = "h"/"x"`

⇒ `sqrt(3)"h" = "x"`  ...(1)

In ΔABD,

`tan 60^circ = "BD"/"AB" = (25 + 25 + "h")/"x"`

`sqrt(3)"x" = 50 + "h"`  ...(2)

From (1) and (2),

`sqrt(3)(sqrt(3)"h") = 50 + "h"`

2h = 50
h = 25
Thus , the height of the cloud above the lake-level is OC = 50 m.