The area of the circular sector is given by:
[tex]\begin{gathered} A=\frac{r^2\theta}{2} \\ where\colon \\ r=radius=17mi \\ \theta=angle=\frac{2\pi}{3} \\ \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} A=\frac{(17^2)\frac{2\pi}{3}}{2} \\ A=\frac{289\pi}{3}\approx302.64 \end{gathered}[/tex]