WOLFRAM|DEMONSTRATIONS PROJECT

Spherical Law of Cosines

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vertex A
θ
1.047
vertex B
θ
1.047
ϕ
1.083
show sphere
Draw a spherical triangle
ABC
on the surface of the unit sphere with center at the origin
O
. Let the sides (arcs) opposite the vertices have lengths
a
,
b
and
c
, and let
A
be the angle at vertex
A
. The spherical law of cosines is then given by
cosa=cosbcosc+sinbsinccosA
, with two analogs obtained by permutations.