Work Shown
r = radius of the circle
theta = central angle in radians
L = arc length
L = (theta/(2pi))*circumference
L = (theta/(2pi))*2pi*r
L = theta*r
This formula will not work if theta is in degrees. The portion theta/(2pi) represents the fractional amount of the circle we want. Recall that 2pi radians = 360 degrees. Conveniently the 2pi terms cancel out.
Plug in the given info so we can find the radius.
L = theta*r
27 = 1.9x
x = 27/1.9
x = 14.2105 approximately
x = 14.2 inches approximately