Question

A circle with circumference 20 has an arc with a 72 central angle. What is the length of the arc?

Answer 1

Answer: 4

Step-by-step explanation:

Answer 2

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.