The formula for the circumference of a circle is

C = nd, where
C = circumference and
d = diameter. It can also be defined as
C = 2mr, where
r = radius. If 360 degrees
= 2m radians, and the formula for arc length is
0 = 7, then determine the length created by a 60-degree central angle in a
circle with a 2-inch diameter and explain how you found it. Answer in 3-5 sentences.

1 answer

To determine the arc length created by a 60-degree central angle in a circle with a 2-inch diameter, we first need to find the radius. The radius \( r \) is half of the diameter, so \( r = 1 \) inch. The formula for arc length \( s \) is given by \( s = r\theta \), where \( \theta \) is the angle in radians. Since 60 degrees is equivalent to \( \frac{\pi}{3} \) radians, we can calculate the arc length as follows:

\[ s = r\theta = 1 \cdot \frac{\pi}{3} = \frac{\pi}{3} \text{ inches} \approx 1.05 \text{ inches.} \]

Thus, the arc length for a 60-degree angle in a circle with a 2-inch diameter is approximately 1.05 inches.