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Question

# Find the distance between the cities. Assume that Earth is a sphere of radius 4000 miles and the cities are on the same longitude (one city is due north of the other).$\begin{matrix} \text{City} & \text{Latitude}\\ \text{Dallas, Texas} & \ {32^{\circ} 47^{\prime} 39^{\prime \prime} \mathrm{N}}\\ \text{Omaha, Nebraska} & \ {41^{\circ} 15^{\prime} 50^{\prime \prime} \mathrm{N}}\\ \end{matrix}$

Solution

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Step 1
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We are given Earth's radius and two cities' coordinates:

\begin{aligned} R &= 4000 \text{ mi}\\ C_1 &= 32^\circ47'39''\text{N}\\ C_2 &= 41^\circ15'50''\text{N} \end{aligned}

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