[tex]\text{ length of arc JM = }12.9\text{ miles}[/tex]Explanation:
arc MK = 90°
arc JMK = 180°
arc MK + arc JM = 180° (sum of arc in a semicircle)
90 + arc JM = 180
arc JM = 180 - 90
arc JM = 90°
To get the length of an arc, we will apply the formula:
[tex]\text{length of an arc = }\frac{\theta}{360}\times2\pi r[/tex]
diameter = JK = 16.4 miles
diameter = 2(radius)
radius = diameter/2
radius = 16.4/2 = 8.2 miles
π = 3.14
Substitute the values:
[tex]\begin{gathered} \text{length of arc JM = }\frac{90}{360}\text{ }\times2\times3.14\times8.2 \\ \text{length of arc JM = }\frac{1}{4}\text{ }\times2\times3.14\times8.2\text{ } \\ \\ \text{length of arc JM = }\frac{1}{2}\times3.14\times8.2\text{ } \end{gathered}[/tex][tex]\begin{gathered} \text{length of arc JM = }12.874 \\ To\text{ the nearest tenth, length of arc JM = }12.9\text{ miles} \end{gathered}[/tex]
