Question

If the angle of elevation of a cloud from a point 200 m above a lake is 30 degree and angle of depression of its reflection in the lake is 60 degree. Then the height of the cloud above the lake is...

Answer 1

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Answer 2

Answer:

400 m

Step-by-step explanation:

After reflection the height of the cloud is from the base of lake is equal to the length of the reflection of cloud from the base of lake

Refer the attached figure

In ΔABC

$tan \theta = \frac{Perpendicular}{Base}$

$tan 30^{\circ} = \frac{BC}{AB}$

$\frac{1}{\sqrt{3}}= \frac{x}{AB}$

$AB= \sqrt{3}x$  --1

In ΔBAD

$tan \theta = \frac{Perpendicular}{Base}$

$tan 60^{\circ} = \frac{BD}{AB}$

$\sqrt{3}= \frac{200+200+x}{AB}$

$\sqrt{3}= \frac{400+x}{AB}$

$AB=\frac{400+x}{\sqrt{3}}$  --2

Equating 1 And 2

$\frac{400+x}{\sqrt{3}}= \sqrt{3}x$

$400+x=3x$

$400=2x$

$x=200$

Height of cloud = 200+x=200+200=400 m

Hence the height of the cloud above the lake is 400m