To find the length of arc [tex]\( s \)[/tex] cut off by the central angle [tex]\( \theta \)[/tex] in a circle with radius [tex]\( r \)[/tex], we can use the formula:
[tex]\[ s = r \cdot \theta \][/tex]
where:
- [tex]\( s \)[/tex] is the length of the arc,
- [tex]\( r \)[/tex] is the radius of the circle,
- [tex]\( \theta \)[/tex] is the central angle in radians.
Given:
- [tex]\( \theta = 2.3 \)[/tex] radians,
- [tex]\( r = 2.2 \)[/tex] feet,
we can now substitute these values into the formula to find the length of the arc [tex]\( s \)[/tex].
[tex]\[ s = 2.2 \cdot 2.3 \][/tex]
Upon multiplying these values, the length of the arc [tex]\( s \)[/tex] is found to be:
[tex]\[ s = 5.06 \text{ feet} \][/tex]
Thus, the length of arc [tex]\( s \)[/tex] is 5.06 feet.
