Question

a ship sailing on a course bearing 025 degrees is 4050 m due south of a lighthouse. if the ship continues on this course, what is the closest distance the ship will come to the lighthouse? (round to the nearest whole number)

Explanation:

Step1: Analyze the angle

The course bearing is \(025\) degrees. The angle between the south - line (from the ship to the lighthouse) and the ship's path is \(25\) degrees.

Step2: Use the sine function

We know the distance of the ship from the lighthouse along the south - line \(d = 4050\) m. The closest distance \(x\) (perpendicular distance from the lighthouse to the ship's path) can be found using the formula \(x=4050\times\sin(25^{\circ})\).
Since \(\sin(25^{\circ})\approx0.4226\), then \(x = 4050\times0.4226\).

Step3: Calculate the value

\(x=4050\times0.4226=1711.53\approx1712\) m.

Answer:

\(1712\) m