1. Spherical Trigonometry deals with triangles drawn on a sphere
Spherical Trigonometry deals with triangles drawn on a sphere. The subject
originated in the Middle East, North Africa and Spain during the 8th to 14th
centuries. It arose to solve an apparently simple problem: Which direction is
Mecca?
The development of this subject lead to improvements in the art of navigation,
stellar map making, geographic map making, the positions of sunrise and sunset,
and improvements to the sundial.

4. Cosine rule for spherical triangles:
The Cosine Rule allows the length of one of the arcs
of a spherical triangle to be evaluated if the other two
arcs and the angle opposite the arc are known.

5. The points B and C are two points on the surface of the Earth.
Point A is the North Pole.
The great circle joining points B and C is the shortest distance between them.
The great circle (in blue) joining B' and C' is the Equator (Latitude 0°).
The great circle (red) joining ABB' is a line of Longitude. It is the Longitude of B.
The great circle joining ACC' is another line of Longitude. It is the Longitude of C.
The length of the great circle arc B'B is the Latitude of point B. The arc B'A is 90°
(Equator to Pole).
The length of the great circle arc C'C is the Latitude of point C. The arc C'A is also 90°.

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