Let us use the equation of the perimeter of a circle to determine the length of the given arc:
[tex]\begin{gathered} 360\degree\Rightarrow2\pi r \\ 126\degree\Rightarrow x \end{gathered}[/tex]
Here, we will use the cross-multiplication to determine the value of the arc 126° at a circle with a radius equal to 14 units.
[tex]\begin{gathered} 360x=126\times2\pi\times14 \\ x=\frac{126}{360}\times14\times2\pi \\ x=0.35\times28\pi \\ x=9.8\pi \end{gathered}[/tex]
To the present problem, let us use π = 3.1415
[tex]\begin{gathered} x=9.8\times3.1415=30.7867 \\ x\cong30.79 \end{gathered}[/tex]
From the solution developed above, we are able to determine that the length of the given arc is equal to:
30.79 units
