Answer: 300/π°, or ~95.49°
Explanation:
In order to find the central angle of the arc, we first find the ratio of the arc length to the circumference of the circle, since it is proportional to the ratio of the central angle to the total inside angle, 360°.
Finding the circumference
Circumference is equal to 2πr, and r (radius) in this case is 3, so
C=2π*3, or 6π
The ratio of the arc length to circumference is then 5/6π
Finding the angle
Since the ratio of lengths and ratio of angles are proportional, we can set up this equation:
5/6π=x/360
solving for x gets us:
x=300/π°, or ~95.49°