Two cities have nearly the same longitude of 90 degrees West

Two cities have nearly the same longitude of 90 degrees West. The latitude of the first city is 22 degrees 06\', and the latitude of the second city is 40 degrees 49\'. Approximate the distance between the two cities if the average radius of the earth is 3955 miles. Round your final answer to the nearest whole mile.

Solution

Answer:  

When the position of a city is given in longitude and latitude you must specify whether it is east or west (longitude) and north or south (latitude).

I will assume that both cities are latitude north.

=> Angle between them is 40° 49\' - 22° 06\' = 18° 43\'

i.e. 18.7166666°

Note: if the cities were on either sides of the equator you would add the angles

Both cities are on the same longitude, hence the same meridian.

This is going to be part of the earth\'s circumference.

=> 2r x (18.716666666/360)......where r is 3955 miles.

=> 2 x x 3955 x (18.716666666/360)

i.e. 1,292 miles.