Answer
$44^o\space N$
Work Step by Step
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:
$=33^o+11^o
\\=44^o N$.
