Question

find the length of an arc of 40 degrees in a circle with an 8 inch radius

Answer 1

a circle is measured in degrees - 360 degrees make 1 circle
BUT there is a less common measure called radians
A circle is made up of 2*pi radians

so 360 degrees = 2*pi radians (i.e. approx. 6.28 radians)

If you measure the angle (theta) in radians then the length of the arc is r*theta

SO
Convert 40 deg to radians, and multiply by the radius

Answer 2

I would add that:

Although the radian measure is 'less common' in everyday usage - it is very common, and essential to the mathematics of Physics