Question

A ship sails on a course bearing 036 degrees is 5500meters due south of a lighthouse.If the ship continues in this course, what is the closest distance the ship will come to the lighthouse?

Answer 1

The closest distance the ship will come to the lighthouse is when it passes directly east or west of the lighthouse.

Since the ship is currently 5500 meters due south of the lighthouse, we have a right triangle with the distance between the ship and the lighthouse being the hypotenuse. The ship's course of 036 degrees is 90 - 36 = 54 degrees from east (or west).

Using trigonometry, we can find the closest distance as follows:
cos(54 degrees) = adjacent/hypotenuse
cos(54 degrees) = x/5500
x = 5500 * cos(54 degrees)
x ≈ 5500 * 0.5878
x ≈ 3234 meters

Therefore, the closest distance the ship will come to the lighthouse is approximately 3234 meters when it passes directly east or west of the lighthouse.