Question

From the top of a light house $60$ meter high, with its base at the sea level, the angle of depression of a boat is ${30}^{\circ }$. The distance of the boat from the foot of the light-house is

• A. $60\sqrt{3}$ meters
• B. $\frac{60}{\sqrt{3}}$ meters
• C. $60$ meters
• D. $30\sqrt{2}$ meters

Answer 1

Answer: (A)

$60\sqrt{3}$ meters

Height of light house $=60$ m
Angle of depression $=$ ${30}^{\circ }$
Let the distance of boat from the light house $=$ $s$
Then, angle of depression $=$ angle of elevation
$\tan \angle$ of elevation $=$ $\frac{\text{height}}{\text{distance}}$
$\tan 30=\frac{60}{s}$
$s=60\sqrt{3}$ m