Answer to Question #135956 in Trigonometry for Marc

Question

A navigator on a ship sailing on a course of 330°at 16 knots (nautical miles per hour) observes a lighthouse, due north of the ship. Fifteen minutes later, the lighthouse is due east of the ship. How far is the lighthouse at that instant?

Answer 1

After 15 minutes, the ship shall cover ;

Distance =$Time$ $×speed(knots)$

$\frac{15}{60} ×16 knots =4nm$

From the initial point and at the point the navigator saw the Lighthouse are corresponding hence the ship was sailing $N30°W$

To get the distance of the Lighthouse ;

$Sin 30°=\frac{opp} {4nm}$

Distance =4 $×$0.5=2nm

=2nm