The question provides the following parameters for the sector under consideration:
[tex]\begin{gathered} \theta=60\degree \\ r=14\text{ in} \end{gathered}[/tex]
PART A: Arc Length
The formula to calculate the Arc Length is given as
[tex]L=\frac{\theta}{360}\times2\pi r[/tex]
Therefore, we can substitute the values for the parameters and solve as
[tex]\begin{gathered} L=\frac{60}{360}\times2\times\pi\times14 \\ L=\frac{1}{6}\times28\pi \\ L=14.66\approx14.7in \end{gathered}[/tex]
The arc length is 14.7 inches.
PART B: Sector Area
The formula to calculate the Arc Length is given as
[tex]A=\frac{\theta}{360}\times\pi r^2[/tex]
Therefore, we can substitute the values and solve as
[tex]\begin{gathered} A=\frac{60}{360}\times\pi\times14^2 \\ A=\frac{1}{6}\times196\pi \\ A=102.6in^2 \end{gathered}[/tex]
The sector area is 102.6 square inches.
