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

The first leg is 200 miles west. On the second leg, the westward component is 30 cos(30°) ≈ 26.0 miles, and the northward component is 30 sin(30°) = 15 miles. The total westward displacement is about 226.0 miles, so the distance from the starting point is √(226.0² + 15²) ≈ 226.5 miles. The correct choice is 226 point 5 mi.

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