Final answer:
Great circle routes are useful because they indicate the shortest distance between two locations on the curved surface of the Earth. They follow the arc of a great circle, which is any circle on the surface of a sphere whose center is at the center of the sphere.
Step-by-step explanation:
Great circle routes are useful because they indicate the shortest distance between two locations on the curved surface of the Earth. Instead of traveling in a straight line, which is not possible due to the solid body of the Earth, an airplane follows the arc of a great circle. A great circle is any circle on the surface of a sphere whose center is at the center of the sphere. For example, Earth's equator is a great circle.
In geometry, the Pythagorean theorem can be used to find the straight-line distance between two points. However, when considering the curved surface of the Earth, great circle routes provide a more accurate measure of distance. The Pythagorean theorem assumes a flat plane, while the great circle takes into account the spherical shape of the Earth.
To find the great circle route between two locations, you can use latitude and longitude coordinates to calculate the angle between the two points and determine the shortest path.