A circle has a radius of 19m. find the radian measure of the central angle θ that intercepts an arc of length 6m.

First, find the perimeter of the circle

p = 2 * π * r

p = 2 * 3,14 * 19

p = 119.32

The perimeter of the circle is 119.32 cm

Second, find the central angle

Comparison of the central angle, full rotation angle, the arc, and the perimeter can be written as

angle / (full rotation angle) = arc/perimeter

angle = arc/perimeter * (full rotation angle)

Input the numbers

angle = arc/perimeter * (full rotation angle)

angle = 6/119.32 * 360°

angle = 6 (360°) / 119.32

angle = 2,160/119.32

angle = 18.1

The central angle would be 18.1°