City A and City B lie on approximately the same meridian Cit

City A and City B lie on approximately the same meridian. City A has latitude 30° N and City B has latitude 24.5° N. Find the distance between the two cities. (The radius of the earth is approximately 3,960 miles and = 3.14. Round your answer to the nearest mile.)

Solution

The circumference of a circle/sphere = 2*pi* r
Therefore the polar circumference of the Earth is 2 x pi x 3960 = 7920 *pi miles
assuming pi = 3.14159
The polar circumference of the Earth is 3.14159 x 7920 = 24881.3928 miles
From North Pole to South Pole though is only half this ie 12440.6964 miles

The polar circumference represents 360 degrees, but the distance from pole to pole only represents a hemishere or 1/2 x 360 = 180 degrees. (It is 90 degrees from the Equator to a Pole)
The difference between Town A and Town B is 5.5 degrees of latitude
Therefore this represents 5.5/180 x 12440.6964 miles
Therefore the distance between the two towns is 5.5/180 x 12440.6964 = 380.132 miles
Rounding up the distance is 380 miles to the nearest whole number.

Nb It is a known fact that one degree of latitude represents \"approx\" 69 miles. 5.5 x 69 = 379.5 miles. Therefore this confirms the above calculation.