Specifying three sides uniquely determines a triangle whose area is given by Heron's formula,
 |
(1) |
where
 |
(2) |
is the semiperimeter of the triangle. Let 
be the circumradius,
then
 |
(3) |
Using the law of cosines
 |  |  |
(4) |
 |  |  |
(5) |
 |  |  |
(6) |
gives the three angles as
 |  |  |
(7) |
 |  |  |
(8) |
 |  |  |
(9) |
See also
AAA Theorem, AAS Theorem, ASA Theorem, ASS Theorem, Heron's Formula, SAS Theorem, Semiperimeter, Triangle
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Cite this as:
Weisstein, Eric W. "SSS Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SSSTheorem.html