Answer to Question #136181 in Trigonometry for jay

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

Solution.

The task is shown in the following picture:

Find the angle α:

$α=360°-330°=30°.$

Find the distance that the ship traveled in 1/4 hour (15 minutes) at a speed 16 nautical miles per hour:

$c=v\cdot t=16\cdot\frac{1}{4}=4$ nautical miles.

Find the distance between the ship and the lighthouse:

$b=c\cdot cos(30°)=4\cdot\frac{\sqrt{3}}{2}=2\sqrt{3}\approx3.46$ nautical miles.

Answer: the lighthouse is about 3.46 nautical miles from the ship.