To find the length of an arc of a sector when given the central angle and the radius, we can follow these steps:
1. Understand the given data:
- Central angle in degrees: 67°
- Radius of the circle: 11 inches
2. Convert the central angle from degrees to radians:
The formula for conversion from degrees to radians is:
[tex]\[
\text{radians} = \text{degrees} \times \left(\frac{\pi}{180}\right)
\][/tex]
So, the central angle in radians is:
[tex]\[
67^\circ \times \left(\frac{\pi}{180}\right) \approx 1.1694 \text{ radians}
\][/tex]
3. Calculate the arc length:
The formula for the arc length (s) is given by:
[tex]\[
s = r \theta
\][/tex]
where [tex]\( r \)[/tex] is the radius and [tex]\( \theta \)[/tex] is the central angle in radians. Substituting the known values:
[tex]\[
s = 11 \times 1.1694 \approx 12.8631 \text{ inches}
\][/tex]
4. Round the arc length to the nearest tenth:
Therefore, 12.8631 rounded to the nearest tenth is:
[tex]\[
12.9 \text{ inches}
\][/tex]
So, the length of the arc is approximately 12.9 inches when rounded to the nearest tenth.
