Answer:
Distance between two cities is 193.94 miles.
Step-by-step explanation:
We have,
Madison and Wisconsin have latitudes 43.0731°N and 45.9172°N respectively.
Thus, their difference is 45.9172°N - 43.0731°N = 2.8441°
We assumed, the diameter of earth is 7917.5 miles.
So, the radius = [tex]\frac{7917.5}{2}[/tex] = 3958.75 miles
So, using the cosine formula, we have,
[tex]a^{2}=b^{2}+c^{2}-2bc\cos A[/tex]
i.e. [tex]a^{2}=3958.75^{2}+3958.75^{2}-2\times 3958.75\times \cos 2.8441[/tex]
i.e. [tex]a^{2}=31343403.13\times 0.0012[/tex]
i.e. [tex]a^{2}=37612.08[/tex]
i.e. a= 193.94 miles.
Hence, the distance between two cities is 193.94 miles.
