Question

From the top of a cliff $200$ metres above the Sea-level the angles of depression of two boats, in the same vertical plane as the observer, are ${45}^0$ and ${30}^0$ respectively. The distance between the boats (in metres) is

• A. $200(\sqrt{3}+1)$
• B. $200(\sqrt{3}-1)$
• C. $400(\sqrt{3}-1)$
• D. $400(\sqrt{3}+1)$

Answer 1

The correct option is B $200(\sqrt{3}-1)$

$\tan {45}^0=\frac{200}{d}$
$\Rightarrow d=200m$

$\tan {30}^0=\frac{200}{a+d}$

$\Rightarrow \frac{1}{\sqrt{3}}=\frac{200}{200+a}$

$\Rightarrow a=200(\sqrt{3}-1)m$