Question

From the top of a light house $60$ metres high with its base at the sea level, the angle of depression of a boat ${15}^{\circ }.$ The distance of the boat from the foot of the light house (in metres) is

• A. $(2+\sqrt{3})60$
• B. $(2-\sqrt{3})60$
• C. $(2+\sqrt{3})30$
• D. none of these.

Answer 1

The correct option is A $(2+\sqrt{3})60$

$\begin{array}{c}In\Delta ABC,\\ \tan {15}^{\circ }=\frac{60}{d}\\ \Rightarrow d=60\cot {15}^{\circ }=60\left(\frac{\sqrt{3}+1}{\sqrt{3}-1}\right)m\end{array}$

or, $d=60\times \frac{(\sqrt{3}+1{)}^2}{3-1}$

or, $d=(2+\sqrt{3})60$.