Distance between Cities Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Assume the radius of Earth is 6400 km. See Example 2. Farmersville, California, 36° N, and Penticton, British Columbia, 49° N

Key Concepts

Great Circle Distance

The great circle distance is the shortest distance between two points on the surface of a sphere. It is calculated using the spherical coordinates of the points, which in this case are the latitudes of the cities. Since both cities lie on the same north-south line, the distance can be determined by the difference in their latitudes, converted into kilometers using the Earth's radius.

Latitude

Latitude is a geographic coordinate that specifies the north-south position of a point on the Earth's surface. It is measured in degrees, with the equator at 0° and the poles at 90° N or S. In this problem, the latitudes of Farmersville and Penticton are essential for calculating the distance between them along the Earth's surface.

Conversion of Degrees to Distance

To convert the difference in latitude (in degrees) to a distance (in kilometers), one can use the formula: distance = (difference in latitude) × (π/180) × radius of Earth. This formula accounts for the curvature of the Earth, allowing for an accurate calculation of the distance between the two cities based on their latitudinal positions.