Specifying three sides uniquely determines a triangle whose area is given by Heron's formula,
(1)
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where
(2)
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is the semiperimeter of the triangle. Let be the circumradius, then
(3)
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Using the law of cosines
(4)
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(5)
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(6)
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gives the three angles as
(7)
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(8)
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(9)
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