If the arc length shown in blue is 15.5 inches, then theta to the nearest hundredth of a radian is?

If you need to refer to the figure you can open the pdf file that I attached.

If you do not know the relationship between arc lengths and angles in radians, you can derive it from the circumference of a circle. This is how:

[2π rad /  2π R] = [x /  arc] , where R is the radius of the circle, arc is the length of the arc, and x is the angle in radians.

You can solve for the angle x.

x = arc / R

In the figure arc = 15.5 inches, R = 12 inches, and theta is the unknown angle. Then:

theta = arc / R = 15.5 / 12 = 1.29167 radians.

Which rounded to the nearest hundreth is 1.29

1.29 radians

 

127 millimeters is the answer