To find the measure of the central angle [tex]\(\theta\)[/tex] for a circle with a given radius and arc length, we can use the relationship between the arc length ([tex]\(s\)[/tex]), the radius ([tex]\(r\)[/tex]), and the central angle in radians ([tex]\(\theta\)[/tex]). The formula is given by:
[tex]\[ s = r \cdot \theta \][/tex]
Where:
- [tex]\( s \)[/tex] is the arc length,
- [tex]\( r \)[/tex] is the radius,
- [tex]\( \theta \)[/tex] is the central angle in radians.
Given:
- The radius [tex]\( r = 5 \)[/tex] feet,
- The arc length [tex]\( s = 7 \)[/tex] feet,
We need to find [tex]\(\theta\)[/tex]. The formula can be rearranged to solve for [tex]\(\theta\)[/tex]:
[tex]\[ \theta = \frac{s}{r} \][/tex]
Substitute the given values into the equation:
[tex]\[ \theta = \frac{7}{5} \][/tex]
Hence, the measure of the central angle [tex]\(\theta\)[/tex] is given by:
[tex]\[ \theta = \frac{7}{5} \][/tex]
Therefore, the correct equation that gives the measure of the central angle is:
[tex]\[ \theta = \frac{7}{5} \][/tex]
