page_title: Solution of triangles
section_title: Two sides and the included angle given (spherical SAS)
hierarchical_section_title: Solution of triangles / Solving spherical triangles / Two sides and the included angle given (spherical SAS)
context_page_description: Solution of triangles is the main trigonometric problem of finding the characteristics of a triangle, when some of these are known. The triangle can be located on a plane or on a sphere. Applications requiring triangle solutions include geodesy, astronomy, construction, and navigation.
context_section_description: Known: the sides a, b and the angle γ between them. The side c can be found from the spherical law of cosines:
  The angles α, β can be calculated as above, or by using Napier's analogies:
  This problem arises in the navigation problem of finding the great circle between two points on the earth specified by their latitude and longitude; in this application, it is important to use formulas which are not susceptible to round-off errors.  For this purpose, the following formulas (which may be derived using vector algebra) can be used:
  where the signs of the numerators and denominators in these expressions should be used to determine the quadrant of the arctangent.
caption: Two sides and a non-included angle given
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