To determine the measure of the central angle, [tex]\(\theta\)[/tex], given the radius of the circle and the length of the arc, we can use the relationship between the arc length, the radius, and the central angle in radians. The formula that relates these quantities is:
[tex]\[
\theta = \frac{\text{arc length}}{\text{radius}}
\][/tex]
Let's plug in the given values:
- The radius of the circle is [tex]\(5 \, \text{ft}\)[/tex].
- The length of the arc is [tex]\(7 \, \text{ft}\)[/tex].
Using the formula:
[tex]\[
\theta = \frac{7 \, \text{ft}}{5 \, \text{ft}}
\][/tex]
This simplifies to:
[tex]\[
\theta = \frac{7}{5}
\][/tex]
Therefore, the equation that gives the measure of the central angle, [tex]\(\theta\)[/tex], is:
[tex]\[
\theta = \frac{7}{5}
\][/tex]
Thus, the correct option is:
[tex]\[
\theta = \frac{7}{5}
\][/tex]
