Q. 114.0( 11 Votes )

If the angle of elevation of a cloud from a point 200 m above a lake is 30° and the angle of depression of its reflection in the lake is 60°, then the height of the cloud above the lake is
A. 200 m

B. 500 m

C. 30 m

D. 400 m

Answer :


A is the position of the cloud, B is the point 200 m above the lake and F is the reflection in the lake.


Here AE = EF


EF = (m + 200) m


In ΔABC



BC = m cot 30° ……………….1


In Δ BCF


CF = 200 + m +200


= (400 + m) meters



BC = (400 + m) cot 60° ………………….2


From 1 and 2


m cot 30° = (400 + m) cot 60°


m =


3 m = (400 + m)

2m = 400

m = 200 m


The height above the cloud above the lake is (200 + 200)m = 400 m.

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