Question

The angle of elevation of a cloud from a point $h$ meters above the surface of a lake is $300$ and the angle of depression of its reflection is $600$. Then the height of the cloud above the surface of the lake is

• A. $\frac{h}{\sqrt{3}}$
• B. $h$
• C. $\sqrt{2}h$
• D. $2h$

Answer 1

Answer: (D)

$2h$

Consider the following diagram with the cloud at the point A
Let the perpendicular distance of the cloud from the the elevation be $x=AC$
Angle ABC$={30}^0$
angle DBC$={60}^0$
Therefore
Consider triangle ABC
$tan{30}^0=\frac{x}{BC}=\frac{1}{\sqrt{3}}$
$BC=\sqrt{3}x$ ...(i)
Similarly consider triangle BDC
$tan{60}^0=\frac{h+h+x}{BC}=\sqrt{3}$
$2h+x=\sqrt{3}BC$ ...(ii)
Substituting the value of BC from equation i we get
$2h+x=\sqrt{3}\sqrt{3}x$
$3x=2h+x$
$h=x$
Therefore the height of the cloud above the surface of the water
$=h+x$
$=2h$
Hence answer is D