Ax=-6.3 sin 23 = -2.46; Ay=6.3 cos 23 = 5.8; Bx=5.7 cos 34 =4.73; By=5.7 sin 34 = 3.19
Sqrt((Bx-Ax)^2 + (By-Ay)^2) = 7.7 units for the magnitude of C.
For the angle measured from the x-axis to vector c, I got -20 which is the angle 20 degrees below the x-axis to vector c using tan.