Answer
$44^{\mathrm{o}}$ N
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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$r=6400$ km, $s=1200$ km
$ s=r\theta,\ \quad$ ... solve for $\theta$
$ 1200=6400\theta$
$\displaystyle \theta=\frac{1200}{6400}=\frac{3}{16}$
see case 2 of converting ....
$\displaystyle \theta=\frac{3}{16}\cdot\frac{180^{\mathrm{o}}}{\pi}\approx$10.7429586587$\approx 11^{o}$
The north-south angle between the two cities is about $11^{0}.$
South Dakota is north of Texas, Madison has the greater latitude
The latitude of Madison is $x=$ (Dallas:$33^{o}$) + $11^{\mathrm{o}}$
The latimde of Madison is $44^{\mathrm{o}}$ N.