A jogger runs 5.0 km on a straight trail at an angle of 60° south of west. What is the southern component of the run rounded to the nearest tenth of a kilometer?

60 ° is the angle between W - direction and the run direction.

You need the angle betwee S-direction and the run direction. This is 90° - 60° = 30 °.

By geometry you can trace a right triangle, where the S-component is the adyacent side and the run is the hypotenuse.

Then cos 30° = adyacent side / hypotenuse = S-component / run

Then S-component = run * cos 30° = 5.0 km * 0.866 = 4.3 km

Answer: 4.3 km