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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?
Solution
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.
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