If the angle of elevation of a cloud from a point h metres above a lake is a and the angle of depression of its reflection in the lake be b, prove that the distance of the cloud from the point of observation is 
In the fig A is the point of observation and C is the position of the cloud.
Let the distance between the cloud and point of observation is x.
In ∆ACD
Sin α = 
CD = AC Sin α ⇒ x Sin α
Cos α = 
AD = x Cos α …………………….(1)
CE = CD + DE = (h + x Sin α)
EF = CE = (h + x Sin α)
DF = DE + EF = (h + h + x Sin α) = (2h + x Sin α) ……………..(2)
In ∆ADF
tan β = 
On substituting value of DF & AD
from above eqns (1) and (2)
tan β = 
= 
2h Cos β + x Sin α Cos β = x Sin 
Cos α
x (Cos α Sin 
- Sin α Cos β ) = 2h Cos β
x = 
On dividing numerator and denominator by Cos α Cos β, we get
x = 
Therefore the distance between cloud and point of observation is 
m
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