## Precalculus (6th Edition)

$\color{blue}{s\approx 5900\text{ km}}$
Since they are in opposite directions from the equator, the central angle between the two cities is: $=41^o+12^o=53^o$ Convert the angle to radians by multiplying $\dfrac{\pi}{180^o}$ to the angle measure to obtain: $=53 \cdot \dfrac{\pi}{180^o}=\dfrac{53\pi}{180}$ RECALL: The length of the arc $(s)$ intercepted by the central angle $\theta$ in a circle of radius $r$ is given by the formula: $s = r\theta$, where $\theta$ is in radian measure. Use the formula above to obtain: $s=r\theta \\s=6400 \cdot \frac{53pi}{180} \\s=5920.156823 \\\color{blue}{s\approx 5900\text{ km}}$