Answer:
arc length = approx. 6/3.14 units
Step-by-step explanation:
Let s represent arc length.
The formula for arc length is thus s = rФ, where Ф is the central angle in radians.
Here we're given the central angle in degrees. We must convert this to radians. The following operations will accomplish that:
72 deg π rad 6 rad
----------- * -------------- = 0 = ----------- = 0.6 rad
1 180 deg 15
We need to evaluate s = rФ, where Ф is the central angle in radians. That works out to be s = r(0.6 rad). We are not given the radius, r, so must calculate it from the known fact that the circumference, C, is 20 units, and that this equals 2π*r. C/(2π) is the radius: 20 units/2π, or 10/π = r.
Returning to s = r(0.6 rad), from above, we get:
s = (10/π)((0.6 rad) = 6/π units, or approx. 6/3.14 units.
