question_answer

From the top of a light house at a height 20 m above sea-level, the angle of depression of a ship is \[30{}^\circ .\]The distance of the ship from the foot of the light house is

A) \[20\,\,m\]                     

B) \[30\,\,m\]

C) \[20\sqrt{3}\]

D) \[30\sqrt{3}\]

Correct Answer: C

Solution :

            

Let AB be the light house with top AB = 20 m

In \[\Delta ABC,\]\[\tan 60{}^\circ =\frac{BC}{AB}\]\[\Rightarrow \]\[\sqrt{3}=\frac{BC}{20}\]

\[\Rightarrow \]                           \[BC=20\sqrt{3}m\]