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  "body": "\n## Summary\n\nSpherical trigonometry studies the relations between the sides and the angles of spherical triangles, the triangles on a sphere bounded by arcs of great circles.\nIts main formulas are the spherical law of cosines, $\\cos c = \\cos a \\cos b + \\sin a \\sin b \\cos \\gamma$, and the spherical law of sines, $\\sin a / \\sin \\alpha = \\sin b / \\sin \\beta = \\sin c / \\sin \\gamma$.\nIt is the part of [[spherical geometry|SQ9RQVANMG]] used in astronomy, geodesy and navigation.\nThe area of a spherical triangle is given by [[Girard's theorem|Y9DM9B0RA3]].\n\n## Explanations\n\n### L1 human\n\nOn a globe, a triangle is made of three arcs of great circles, and its sides are measured as angles seen from the centre of the Earth.\nSpherical trigonometry answers questions such as: given two sides and the angle between them, how long is the third side?\nA pilot uses it to find the great-circle distance between two airports from their latitudes and longitudes.\nFor small triangles the formulas reduce to the plane ones, which is why plane trigonometry works on a field but not across an ocean.\n",
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