Question

At a point A 20 meters above the level the level of water in a lake , the angle of elevation of a cloud is 30${}^0$ . The angle of depression of the reflection of the cloud in the lake , at A is 60${}^0$ Find the distance of the cloud from A.

Answer 1

$\tan {30}^0=\frac{EC}{AD}=\frac{1}{\sqrt{3}}\left(ED=h\right)$

$\Rightarrow AD=h\sqrt{3}$---------------$\left(1\right)$

$\tan {60}^0=\frac{FD}{AD}=\sqrt{3}$

$FD=h+40$

$AD=\frac{h+40}{\sqrt{3}}$----------------$\left(2\right)$

$h\sqrt{3}=\frac{h+40}{\sqrt{3}}$

$3h=h+40$

$2h=40$

$h=20m$

$EC=h+20=20+20=40m$

Hence, the height of the cloud from the surface is $40cm.$