Given the word problem, we can deduce the following information:
Radius of a circle = 6 feet
Arc length = 6 feet
To determine the central angle, we use the formula:
[tex]\theta=\frac{L}{r}(\frac{360}{2\pi})[/tex]
where:
L=arc length
r=radius
θ= central angle in degrees
We plug in what we know:
[tex]\begin{gathered} \theta=\frac{L}{r}(\frac{360}{2\pi}) \\ =\frac{6}{6}(\frac{360}{2\pi}) \\ \text{Simplify} \\ \theta=\frac{180}{\pi} \\ \\ \text{Calculate} \\ \theta=57.30\degree \end{gathered}[/tex]
Therefore, the angle is 57.30°.
