Find the number of inches in the radius of a circle if a central angle of measure 2 radians intercepts an arc of length 3/4 inch.

I used the formula s = r * theta
3/4 = r * 115 because on the unit circle 2 radians is about 115 degrees but when I solve for r I get 0.006521, is that correct?

no. The angle must be in radians.

The circumference of a circle is not 360r, it is 2πr.