Q19 of 25 Page 9

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 find the height of the cloud above the lake.

To find:


The height of the cloud.


Explanation:



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°



3 m = (400 + m)


m = 200 m


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


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