Question

The angle of depression of a boat B from the top K of a cliff HK 300 metres high is ${30}^{\circ }$.

Find the distance of the boat from the foot H of the cliff.

• A. $300\sqrt{3}m$
• B. $400\sqrt{3}m$
• C. $500\sqrt{3}m$
• D. $600\sqrt{3}m$

Answer 1

The correct option is A $300\sqrt{3}m$

Let the required distance $BH=x$ metres
HK is the cliff and $\angle LKB$ is the angle of depression of B from K
Then $\angle KBH=\angle LKB={30}^{\circ }$ $(\because LM\parallel BH,alt.\angle s)$
$\therefore$ In $\Delta BKH$
$\tan {30}^{\circ }=\frac{KH}{BH}=\frac{300}{x}$
$\Rightarrow x=\frac{300}{\tan {30}^{\circ }}=\frac{300}{\frac{1}{\sqrt{3}}}=(300\times \sqrt{3})$ metres = $300\sqrt{3}m$