If tan (theta) = 12/5 = 2.4
then the arc tangent (2.4) = theta = 67.38 Degrees AND if we add 180 degrees to this, we find that the arc tangent (2.4) ALSO equals 247.38
the cosine (67.38) = 0.38462 which is greater than zero, so we must look up the cosine (247.38) which equals -0.38462 and is less than zero which is our answer 247.38 degrees.
see the graphic I have attached.