Explanation:
Part 1:
The formula to calculate the area of a sector is given below as
[tex]A_{sector}=\frac{\theta}{360}\times\pi r^2[/tex]
The formula to calculate the length of an arc is given below as
[tex]L_{arc}=\frac{\theta}{360}\times2\pi r[/tex]
Part 2:
The given dimensions are
[tex]\begin{gathered} \theta=160^0 \\ r=5in \end{gathered}[/tex]
To figure out the length of the arc, we will use the formula below
[tex]\begin{gathered} A_{sector}=\frac{\theta}{360}2\pi r \\ A_{sector}=\frac{160}{360}\times2\pi\times5 \\ A_{sector}=13.96in^ \end{gathered}[/tex]
Hence,
The length of the arc will be
[tex]\Rightarrow L_{arc}=13.96\imaginaryI n^[/tex]
To figure out the area of the sector, we will use the formula below
[tex]\begin{gathered} A_{sector}=\frac{\theta}{360}\pi r^{2} \\ A_{sector}=\frac{160}{360}\times\pi(5^2) \\ A_{sector}=34.91in^2 \end{gathered}[/tex]
Hence,
The area of the sector will be
[tex]\Rightarrow A_{sector}=34.91\imaginaryI n^2[/tex]
