Homework Help: Vectors-magnitude problem

A man in search of his dog drives first 12.7 mi northeast, then 17.7 mi straight south, and finally 7.97 mi in a direction 30.3° north of west.

a) What is the magnitude of his resultant displacement?

okay so i wont explain everything i did but im pretty sure i got the right numbers.
for my resultant vector i get (2.09899, -4.63). the magnitude should be 5.08357. but its somehow not the right answer and im not sure what i did wrong.

whats weird is that i needed to find the position of this vector which would be arctan(2.09899/-4.63) + 360. which would be 294.07136 degrees. THIS IS THE CORRECT ANGLE!! so then wouldn't that mean that (2.09899, -4.63) are the right x and y values?!?!?

what am i doing wrong?

thanks for any help!!