A ship travels 60 miles in the direction S 45° E, then travels 150 miles in the direction S 20° W. What is the distance, x, from the starting location?

The two directions are 65° apart: S 45° E and S 20° W lie on opposite sides of south. For the resultant distance, use the law of cosines with the angle between the travel vectors: x² = 60² + 150² + 2(60)(150)cos(65°). This gives x ≈ 183.60 miles, so the distance is 183.60 mi.

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