Spherical Right Triangles

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Draw a spherical triangle on the surface of a unit sphere centered at . Denote the arcs opposite the corresponding vertices as , , . Let , , be the angles at the vertices , , . Suppose , so that these become spherical right triangles. The following relations are then valid:


Contributed by: Izidor Hafner (March 2017)
Open content licensed under CC BY-NC-SA



Let be the orthogonal projection of onto the edge . Let be the orthogonal projection of onto . Then , , but also . Thus .

, , but also . Thus .


[1] Wikipedia. "Spherical Law of Cosines." (Mar 21, 2017) en.wikipedia.org/wiki/Spherical_law_of _cosines.

[2] Wikipedia. "Spherical Trigonometry." (Mar 21, 2017) en.wikipedia.org/wiki/Spherical_trigonometry.

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