Joe and jill set sail from the same point, with joe sailing in the direction s4 degrees e and jill sailing in the direction s9 degrees w. after 4 hr, jill was 2 miles due west of joe. how far had jill sailed?

The angle between Joe and Jill's initial directions is 4° +9° = 13°. The angle Joe measures after 4 hours between Jill's position and their starting point is 90° -4° = 86°. The law of sines can be used to find Jill's travel distance.

Jill's distance = (distance to Joe)*(sin(86°)/sin(13°))
Jill's distance = (2 mi)*0.99756/0.22495
Jill's distance = 8.869 mi

Jill had sailed 8.9 miles in 4 hours.