Question

If the angle of elevation of a cloud from a point is h m above a lake is alpha and the angle of depression of its reflection is beta .prove that the distance of the cloud from the point of observation is 2hsec alpha÷tan alpha -tan beta

Answer 1


Let CE be the surface of the lake and B be the position of point of observation
Given BC = h metres
Hence DE = h metres
Let A be the position of the cloud and F be the reflection of the cloud in the lake
That is AE = EF
Given ∠ABD = α and ∠DBF = β
Let AD = x metres and BD = y metres
From the figure, AE = x + h
In right ΔADB,

Similarly in right ΔBDF, BD = x
DF = DE + EF = h + (x +h) = x +2h


But height of the cloud = x + h