Question

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

Answer 1

Given that $AO=20m\angle BAC={30}^{\circ }\angle BAD={60}^{\circ }$

So $AO=BD=20m$

In $△BAD$

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

$\frac{\sqrt{3}}{1}=\frac{20}{AB}\Rightarrow AB=\frac{20}{\sqrt{3}}$

In $△BAC,$

$\cos {30}^{\circ }=\frac{AB}{AC}$

$\frac{\sqrt{3}}{2}=\frac{\frac{20}{\sqrt{3}}}{AC}$

$\Rightarrow AC=\frac{\frac{20}{\sqrt{3}}}{\frac{\sqrt{3}}{2}}=\frac{40}{3}=13.333m$

Distance of cloud from point A is 13.333m