Question

A woman leaves home and walks 7 miles west, then 4 miles southwest. How far from home is she? (Round your answer to three decimal places.)

In what direction must she walk to head directly home?

Answer 1

The woman is approximately 7.81 miles away from home, and she must walk east and northeast to head directly home.

Step-by-step explanation:

To find the distance from home, we use the Pythagorean theorem. The vertical and horizontal distances form a right triangle, with the 7-mile displacement west as the horizontal leg and the 4-mile displacement southwest as the diagonal leg. The vertical leg can be calculated using trigonometric functions:

Vertical Distance (y) = 4 * sin(45°) = 4 * 0.7071 = 2.8284 miles

Using the Pythagorean theorem:

Distance from Home = sqrt((7)^2 + (2.8284)^2) = sqrt(49 + 7.9997) ≈ 7.81 miles

To head directly home, the woman must walk in the opposite direction. Since she walked west and southwest, she needs to walk east and northeast to head directly home.