1. 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





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  • By: anil on 05 May 2019 01.50 am
    Given : F is the reflection of cloud at point A and CE = 200 m To find : AE = ? Solution : In $$ riangle$$ ABC, => $$tan(30^circ)=frac{AC}{BC}$$ => $$frac{1}{sqrt3}=frac{x}{BC}$$ => $$BC=xsqrt3$$ -------------(i) Similarly, in $$ riangle$$ BCF, => $$tan(60^circ)=frac{CF}{BC}$$ => $$sqrt3=frac{x+200+200}{xsqrt3}$$    [Using (i)] => $$3x=x+400$$ => $$3x-x=2x=400$$ => $$x=frac{400}{2}=200$$ m $$ herefore$$ AE = AC + CE = $$200+200=400$$ m => Ans - (D)
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