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The angle of elevation of a cloud from a point 200m above the lake is 30 degree and the angle of deppression of its reflection in the lake is 60 degree find the height of the cloud above the lake.

A is the position of the cloud , B is the point 200m above the lake and F is the reflection of A in the lake.
Now, AE = EF
=> EF = (200 + m)
Now, from triangle ABC we have,
BC = m cot 300 --- (i)
in triangle CFB we have,
CF = 200 + (200 + m)
= (400 + m) ms
so, BC = (400 + m) cot 600 --(ii)
From (i) and (ii) we get,
(400 + m) cot 600 = m cot 300
=> (400 + m) x 1/root3 = m x root 3
=> 400 + m = 3m
=> 2m = 400
=> m = 200
Hence, height of the cloud = AE = 200 + m = 200 + 200 = 400 metres


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