Question

In geography, latitude gives the north-south position of a point on Earth's surface. latitude is an angle, ranging from 0 degrees at the equator to 90 degrees N at the North Pole and 90 degrees S at the South Pole. The overland distance between points on Earth's surface is an arc, with the central angle measured from Earth's center. The formula of the length, L, of an arc with central angle x degrees on a circle with radius r is :

L= 2\pie times x/360

Suppose that two cities have the same longitude, which gives the east-west position of a point on Earth's surface. One has latitude 19 degrees N, and the other has a latitude 26 degrees S. Assume Earth is a sphere with a radius of 6,380 km. Find the distance between the two cities to the nearest kilometer.

Answer 1

The distance between the two cities is 9,547 kilometers. This can be calculated by using the formula L= 2\pie times x/360, where x is the central angle calculated by subtracting the two latitudes (-19 degrees and -26 degrees), which gives a central angle of 7 degrees. Plugging this into the formula and using the radius of 6,380 km, the distance is calculated to be 9,547 kilometers.