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

Given : F is the reflection of cloud at point A and CE = 200 m

To find : AE = ?

Solution : In $$\triangle$$ ABC,

=> $$tan(30^\circ)=\frac{AC}{BC}$$

=> $$\frac{1}{\sqrt3}=\frac{x}{BC}$$

=> $$BC=x\sqrt3$$ -------------(i)

Similarly, in $$\triangle$$ BCF,

=> $$tan(60^\circ)=\frac{CF}{BC}$$

=> $$\sqrt3=\frac{x+200+200}{x\sqrt3}$$    [Using (i)]

=> $$3x=x+400$$

=> $$3x-x=2x=400$$

=> $$x=\frac{400}{2}=200$$ m

$$\therefore$$ AE = AC + CE

= $$200+200=400$$ m

=> Ans - (D)