Please Help. City A is due North of city B. The latitudes of city A and city B are 54° N and 45° N, respectively. What is the North-South distance between the two cities? The radius of the Earth is 6400km.

Explanation:

For now, we're going to ignore the latitudes. Let's just compute the circumference of the earth. The earth is approximately a sphere. This means we can compute the total distance we would travel if we traveled along this particular longitude (north/south) line. We travel around the entire earth staying only on this line.

C = circumference = perimeter around the circle

C = 2*pi*r

C = 2*pi*6400

C = 40,212.3859659493

This value is approximate. I used the calculator's stored version of pi rather than something like pi = 3.14 to get the most accuracy possible.

We'll keep this value of C in mind for later.

Now we consider the latitudes given to us.

The difference in these latitudes is 54-45 = 9 degrees.

If we let point M be at the center of the earth, then angle BMA is equal to 9 degrees. This represents 9/360 = 1/40 of the full circle's perimeter. So the curved distance between the cities is 1/40 of that C value we calculated earlier.

distance between the two towns = (1/40)*C

distance = (1/40)*(40,212.3859659493)

distance = 1,005.30964914873

If we round to the nearest km, then we get roughly 1005 km

This converts to about 6216.81878 miles

The result we get is going to be a bit off because 6400 km isn't the exact radius of the earth (it's only an approximation). The same can be said about the value of pi used. Though we can get closer enough to get a good idea of what's going on.

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