A ship travels 200 miles due west, then adjusts its course 30° north of west. The ship continues on this course for 30 miles. Approximately how far is the ship from where it began?

The second leg adds about 30 cos 30° = 26.0 miles west and 30 sin 30° = 15 miles north. The total displacement is therefore about 226 miles west and 15 miles north. Using the Pythagorean theorem, the distance from the starting point is √(226² + 15²) ≈ 226.5 miles, so the answer is 226.5 mi.

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