A cyclist travels 5 miles in the direction N 30° E, then travels 3 miles in the direction N 70° E. Which equation measures the cyclist’s distance, x, from the starting point?

The two directions differ by 70° − 30° = 40°. In the triangle formed by the two legs and the cyclist’s direct distance x, the included angle is 180° − 40° = 140°, because the first leg points back toward the start at that vertex. By the Law of Cosines, x² = 5² + 3² − 2(5)(3)cos(140°), which is choice D.

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