13.61 km
Explanation
the length of an arc is given by:
[tex]\begin{gathered} arc\text{ length=}\frac{\theta}{360}\cdot2\pi r \\ \text{where } \\ \theta\text{ is the angle} \\ r\text{ is the radius} \end{gathered}[/tex]
Step 1
let
[tex]\begin{gathered} \theta=30\text{ \degree} \\ r=\text{ 26 }km \end{gathered}[/tex]
now, replace in the formula
[tex]\begin{gathered} arc\text{ length=}\frac{\theta}{360}\cdot2\pi r \\ arc\text{ length=}\frac{30}{360}\cdot2\pi(26)km \\ arc\text{ length=}\frac{30}{360}\cdot2\pi(26)km \\ arc\text{ length=}\frac{1560\pi}{360}km \\ arc\text{ length=}\frac{1560\pi}{360}km \\ arc\text{ length=13.61 }km \end{gathered}[/tex]
therefore, the answer is
13.61 km
I hope this helps you
