Question

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

Answer 1

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°