SOLUTION: When a plane flies directly from New York to London and then to Nairobi and
back to New York, it flies along the sides of a spherical triangle, approximately following the surface
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back to New York, it flies along the sides of a spherical triangle, approximately following the surface
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Question 356855: When a plane flies directly from New York to London and then to Nairobi and
back to New York, it flies along the sides of a spherical triangle, approximately following the surface of Earth. On a sphere, the shortest path between two points is along an arc of a great circle. A great circle is obtained when a plane through the center of the sphere intersects the
sphere. (An example of a great circle is the equator.) To obtain a great circle through two given points on the sphere, we need consider only a plane through the two points and the center of the sphere. A spherical triangle consists of three points on the sphere and arcs of great circles (the shortest path) connecting the points.
a. How many great circles go through the North Pole and the South Pole on the globe?
b. Describe a spherical triangle that has one vertex at the North Pole and the other two vertices on the
equator.
c. Is there a spherical triangle with three right angles? If so, find one. Answer by Alan3354(69443) (Show Source):
