we have that
if cos(∅)=x----------------> arccos (x)=∅
then
cos(∅)=0.63
∅=arccos(0.63)-------------> ∅=50.95°
The question does not specify in which quadrant the angle is, since the cosine function is positive, the angle must be in the first quadrant or in the fourth quadrant
if it is in the first quadrant the angle is 50.95°
and
if it is in the fourth quadrant the angle is (360°-50.95°)=309.05°