Jill walks 10 miles at 40 degrees south of west. How far west of her starting point does she end up?

Draw a diagram

The distance West is 10cos(40)

To determine how far west Jill ends up, we need to consider the components of her displacement.

Jill walks 10 miles at 40 degrees south of west. This means she travels 10 miles in the southwest direction, deviating 40 degrees below the west direction.

To find the westward component, we can use trigonometry. We can split the displacement into two components: east-west and north-south.

The westward component can be found using the cosine function:

cos(40) = adjacent/hypotenuse,
cos(40) = westward displacement/10 miles.

To find the westward displacement, we rearrange the equation:

westward displacement = 10 miles * cos(40).

Using a calculator to evaluate the expression, we find:

westward displacement ≈ 7.64 miles.

Therefore, Jill ends up approximately 7.64 miles west of her starting point.