Serway & Jewett — Motion in Two Dimensions: Problem 32

You are participating in a summer internship with the Coast Guard. You have been assigned the duty of determining the direction in which a Coast Guard speedboat should travel to intercept unidentified vessels. One day, the radar operator detects an unidentified vessel at a distance of 20.0 km from the radar installation in the direction 15.0° east of north. The vessel is traveling at 26.0 km/h on a course at 40.0° east of north. The Coast Guard wishes to send a speedboat, which travels at 50.0 km/h, to travel in a straight line from the radar installation to intercept and investigate the vessel, and asks you for the heading for the speedboat to take. Express the direction as a compass bearing with respect to due north.