Question

Bill walks 4 miles east, 5 miles north, and 7 miles west. How many miles is he, in a direct line, from his starting point?

Answer 1

5.83 miles

Explanation:

Bill's net distance west of his starting point is -4+7 = 3 miles. His net distance north of his starting point is 5 miles. The straight-line distance will be the hypotenuse of a right triangle with legs 3 miles and 5 miles. That distance is given by the Pythagorean theorem:

d² = (3 mi)² +(5 mi)² = 34 mi²

d = √34 mi ≈ 5.83 mi

Bill is 5.83 miles on a direct line from his starting point.

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The attached calculator screenshot shows the sum of the travel distances. The angles are bearings measured clockwise from north. The angle of the sum indicates Bill is about 31° west of north relative to his starting point.