Question

A cruise ship sets a course N50°E from an island to a port on the mainland, which is c = 170 miles away. After moving through strong currents, the ship is off course at a position P that is N36°E and a = 90 miles from the island, as illustrated in the figure.

(a) Approximately how far is the ship from the port? (Round your answer to one decimal place.)

(b) In what direction should the ship head to correct its course? (Round your answer to the nearest whole number.)

Answer 1

using the law of cosines, the ship's distance x from the port is

x^2 = 170^2 + 90^2 - 2*170*90 cos 14°

Now just figure the coordinates of the ship and port to get the desired course.

That assumes that there are no cross currents for the rest of the trip.