## Precalculus (6th Edition)

$44^o\space N$
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. The radius of Earth is around $6400$ km., and the distance between the two cities (which is $s$) is 1200 km. Use the formula above to obtain: $s=r\theta \\1200=6400 \cdot \theta \\\dfrac{1200}{6400} = \theta \\0.1875=\theta \\0.1875 \cdot \dfrac{180^o}{\pi}=\theta \\10.74295866^o=\theta \\\theta \approx 11^o$ Since Dallas is found below South Dakota in the map, then the latitude of Madison must be 11 degrees higher than Dallas. Thus, the latitude of Madison must be: $=33^o+11^o \\=44^o N$.