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Question 356839: 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, as shown in Figure 11-28(a), 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 great
circle through points A and B is shown in Figure 11-28(b). 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):
You can put this solution on YOUR website! a. How many great circles go through the North Pole and the South Pole on the globe?
An infinite number. Any plane that contains the line between the 2 poles intersects the sphere in a great circle.
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b. Describe a spherical triangle that has one vertex at the North Pole and the other two vertices on the equator.
The 2 angles on the equator are right angles. The third can be from >zero to <180 degrees
c. Is there a spherical triangle with three right angles? If so, find one.
As in b above, if the angle at the pole is also 90 degs.
For example, the pole, and longitude 0 degs and 90 degs on the equator.
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