ANSWER
2π/3 rad ≈ 2.1 rad
EXPLANATION
The arc length of a portion of a circle with central angle θ and radius r is,
[tex]s=r\cdot\theta[/tex]In this case, we know that the arc length is s = 10π/3, the radius is 5, and we have to find the central angle. Solving the equation above for θ,
[tex]\theta=\frac{s}{r}[/tex]Substitute the known values and solve,
[tex]\theta=\frac{\frac{10\pi}{3}}{5}=\frac{10\pi}{3\cdot5}=\frac{10\pi}{15}=\frac{2\pi}{3}\approx2.1[/tex]Hence, the angle is 2π/3 radians or 2.1 radians - this last result is rounded to the nearest tenth.