hello
to solve this problem, we need the formula of length of an arc
[tex]\begin{gathered} L_{\text{arc}}=\frac{\theta}{360}\times2\pi r \\ \end{gathered}[/tex]
t find the value of angle JM, we should take into cognizance that the sum of angles in a circle is equal to 360 degree and angle on a straight line is equal to 180 degree
[tex]\begin{gathered} jk+jm+mk=360 \\ 180+jm+90=360 \\ 270+jm=360 \\ jm=360-270 \\ jm=90 \end{gathered}[/tex]
now we know the value of angle jm, let's find the length of the radius
[tex]\begin{gathered} \text{radius}=\frac{\text{diameter}}{2} \\ \text{diameter}=16.4 \\ \text{radius(r)}=\frac{16.4}{2}=8.2\text{miles} \end{gathered}[/tex]
with all the necessary informations or data required, we can now proceed to solve for the length of arc jm
[tex]\begin{gathered} L_{\text{arc}}=\frac{\theta}{360}\times2\pi r \\ L_{\text{arc}}=\frac{90}{360}\times2\times3.14\times8.2 \\ L=12.87\text{miles} \end{gathered}[/tex]
from the calculations above, the length of the arc is equals to 12.87 miles
