Question

PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! SUPER IMPORTANT QUESTION!!!

Madison, Wisconsin has a latitude of 43.0731° N and Eagle River, Wisconsin has a latitude of 45.9172° N, Assuming the Earth is a sphere with a diameter of 7,917.5 miles, what is the distance between these 2 cities along the arc of the Earth's surface? Show all work for full credit.

Answer 1

Distance between two cities is 193.94 miles.

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 =
`(7917.5)/(2)` = 3958.75 miles

So, using the cosine formula, we have,

`a^(2)=b^(2)+c^(2)-2bc\cos A`

i.e.
`a^(2)=3958.75^(2)+3958.75^(2)-2* 3958.75* \cos 2.8441`

i.e.
`a^(2)=31343403.13* 0.0012`

i.e.
`a^(2)=37612.08`

i.e. a= 193.94 miles.

Hence, the distance between two cities is 193.94 miles.