Question

the angle of elevation of the cloud from a point 60 m above lake is 30 degrees and the angle of depression of the reflection of the cloud in the lake is 60 degree .find the height of the cloud from the surface of the lake?

Answer 1

CPE = 30

DPE = 60

CE = CF - EF = h - 60

DE = DF + EF = h + 60 

tan 30 = CE/PE

$\frac{1}{ \sqrt{3} } = \frac{h-60}{PE}$

PE = √3(h-60) ............  i 

tan 60 = DE/PE

$\sqrt{3} = \frac{h+60}{PE}$

PE = $\frac{h+60}{ \sqrt{3} }$      ............ .ii


from i and ii we get

$\frac{h+60}{ \sqrt{3} }$ = √3(h-60)

h + 60 = 3h - 180 

⇒ 2h = 240

⇒ h = 120 m ANSWER

Answer 2

Answer:

Let A be the cloud and D be its shadow.

BC = 60 m  

Height of cloud = h m .

Total height of cloud = h + 60 m  

In  Δ ABE

h / x = tan 30

x = h √ 3

In Δ BDE

h + 60 + 60 / x  = tan 60

h + 120 = x √ 3

2 h = 120

h = 60 m .

Therefore , height of cloud from surface of water = ( 60 + 60 ) = 120 m .