Question

From the top of a lighthouse, an observer looking at a ship makes angle of depression of 60°. If the height of the lighthouse is 90 metre, then find how far the ship is from the lighthouse.

\[\left( \sqrt{3} = 1.73 \right)\]

Answer 1

Let AB be the lighthouse and C be the position of the ship from the lighthouse.
Suppose the distance of the ship from the lighthouse be x m.

In right ∆ABC,
\[\tan60^\circ = \frac{AB}{BC}\]
\[ \Rightarrow \sqrt{3} = \frac{90}{x}\]
\[ \Rightarrow x = \frac{90}{\sqrt{3}} = 30\sqrt{3}\]
\[ \Rightarrow x = 30 \times 1 . 73 = 51 . 9 m\]

Thus, the ship is 51.9 m away from the lighthouse.