Question
If the angles of elevation of a cloud from a point h metres above a lake is α and the angle of depression of its reflection in the lake is β, prove that the height of the cloud is
Solution
Let AB be the surface of the lake and P be the position of the observer h metres above the lake. Let C be the cloud and C be the reflection in the cloud, then CB = C'B. It is also given that the angle of elevation of cloud from a point h m above a lake is α and angle of depression of its reflection is β.
i.e., ∠CPQ = α
and ∠QPC' = β.
Let CQ = x m
Then
CB = CQ + BQ
= CQ + PA
= x + h
In right triangle PQC, we have
In right triangle PQC', we have
Comparing (i) and (ii), we get
Hence, the height of the cloud
Hence, the height of the cloud is
