Answer
5920 km
Work Step by Step
Arc length s (for central angle $\theta$):$ \quad s=r\theta$, where $\theta$ is in radians
Converting between Degrees and Radians
1. Multiply a degree measure by $\displaystyle \frac{\pi}{180}$ radian and simplify to convert to radians.
2. Multiply a radian measure by $\displaystyle \frac{180^{\mathrm{o}}}{\pi}$ and simplify to convert to degrees.
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$12^{\mathrm{o}}S=-12^{\mathrm{o}}N$
$\theta=41^{\mathrm{o}}-(-12^{\mathrm{o}})=53^{\mathrm{o}}$
we convert this to radians
(conversion, case 1)
$\theta=53 (\displaystyle \frac{\pi}{180}$ rad $)=\displaystyle \frac{53\pi}{180}$ rad
Arc length s, with r=6400 km
$ s=r\displaystyle \theta=6400(\frac{53\pi}{180})\approx$5920.15682276$\approx$5920 km
