Final answer:
Great circle routes appear as straight lines on gnomonic projections. Great circles represent the shortest path between two points on a sphere, such as Earth, and are crucial for navigation and travel.
Step-by-step explanation:
On which one of the following projections do great circle routes appear as straight lines? The correct answer is (a) gnomonic projection. A gnomonic projection is a type of map projection that is created by projecting points from a globe onto a piece of paper that touches the globe at a single point. This type of projection results in great circles being represented as straight lines on the map. Great circles are the shortest path between two points on a sphere, such as when traveling on the curved surface of planet Earth. Examples of great circles include the equator and meridians.
Travel on the curved surface of the Earth along a great circle is the shortest route between two points. If you were to fly from Chicago to Rome, the flight path would follow an arc of a great circle. On a Mercator projection, these routes are shown as curved lines because Mercator projections preserve angles and shapes but not distances or areas, especially near the poles. In contrast, gnomonic projections show the true path of great circles as straight lines, simplifying the navigation process.