A ship is being pulled by two tugboats. The smaller tugboat is 13 degrees off the port bow and the larger tugboat is 20 degrees off the starboard bow. The larger one pulls twice as hard as the smaller tugboat. In what direction will the ship move?

Answer 1

Just for ease of notation, say the reference direction is 0°, and the forces have magnitude 1 and 2. So, we need to add

1 @ 13° = (0.9743,0.2250)
2 @ -20° = (0.9397,-0.6840)
add them up to get
(1.914,-0.459) = 1.968 @ -13.5°

You can determine whether that's port or starboard.