Question

The angle of depression of a ship from the top of a lighthouse is 60º. If the lighthouse is $60\sqrt{3}m$, then the distance of the ship from the foot of the lighthouse is

• A. 60 m
• B. 30 m
• C. $60\sqrt{3}m$
• D. 180 m

Answer 1

The correct option is A 60 m

Let PQ be the lighthouse of length $60\sqrt{3}m$ and R be the position of the ship.
$In\Delta PQR,$
$\tan {60}^{\circ }=\frac{PQ}{PR}$
$\Rightarrow \tan {60}^{\circ }=\frac{60\sqrt{3}}{PR}$
$\Rightarrow \sqrt{3}=\frac{60\sqrt{3}}{PR}$
$\Rightarrow PR=60m$
Thus, the distance between the ship and the foot of the lighthouse is 60 m.
Hence, the correct answer is option (a).