So far, I solved for the components of the vector of B, and the vector of A.

Vector A:
cos 40 = x/360; x = 276
sin 40 degrees = y/360; y = 231
= (276, 231)

Vector B:
I guess to use sin, cos, tan I need a right angle. So I do the bottom of B to do it. (123+40=163; 180-163=17 degrees)
cos 17 = x/880; x = 842
sin 17 = y/880; y = 257
= (842, 257)

Vector B - Vector A = (842, 257) - (276, 231) = (566, 26)

Which is wrong. What am I doing wrong? Should I be doing Vector B a different way? Or did I do the entire thing wrong?

What you've forgotten to do is to take into account that the B x coordinate should be negative because you have crossed the perpendicular to the origin.

Could you clarify exactly what vector they want you to find or post the answer so I can work it out. Are you sure you're supposed to only subtract a from b?