Need help finding an angle in degrees

A map suggests that Atlanta is 731 mi in a direction of 4.90° north of east from Dallas. The same map shows that Chicago is 562 miles in a direction of 21.0° west of north from Atlanta. Modeling the Earth as flat, use this information to find the displacement from Dallas to Chicago.

magnitude

Now I've drawn this out and I get distance between dallas/chicago = 774 miles.

Now as far as the angles inside the triangle I used the law of sines.

sin(a)/A = sin(b)/B = sin(c)/C I know the answer is between 41.2 and 48.6 but I think I made a calculation error somewhere because I keep slightly getting the wrong answer.

Ive got less than one hour.