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Spherical Law of Sines
Draw a spherical triangle
on the surface of the unit sphere with center at the origin
. Let the sides (arcs) opposite the vertices have lengths
,
and
, and let
,
and
be the angles at the vertices
,
and
. The spherical law of sines states that
.
Contributed by:
Izidor Hafner
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Let
be the orthogonal projection of
onto the plane
. Let
and
be the orthogonal projections of
onto the lines
and
, respectively. Then
,
,
,
and
, so
.
References
[1] Wikipedia. "Spherical Law of Cosines." (Feb 22, 2017)
en.wikipedia.org/wiki/Spherical_law_of _cosines
.
[2] Wikipedia. "Spherical Trigonometry." (Feb 22, 2017)
en.wikipedia.org/wiki/Spherical_trigonometry
.
RELATED LINKS
Spherical Trigonometry
(
Wolfram
MathWorld
)
Spherical Triangle Solutions
(
Wolfram Demonstrations Project
)
PERMANENT CITATION
Izidor Hafner
"
Spherical Law of Sines
"
http://demonstrations.wolfram.com/SphericalLawOfSines/
Wolfram Demonstrations Project
Published: February 24, 2017
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