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Newton's Formulas


Let a triangle have side lengths a, b, and c with opposite angles A, B, and C. Then

(b+c)/a=(cos[1/2(B-C)])/(sin(1/2A))
(1)
(c+a)/b=(cos[1/2(C-A)])/(sin(1/2B))
(2)
(a+b)/c=(cos[1/2(A-B)])/(sin(1/2C)).
(3)

See also

Mollweide's Formulas, Triangle

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References

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 146, 1987.

Referenced on Wolfram|Alpha

Newton's Formulas

Cite this as:

Weisstein, Eric W. "Newton's Formulas." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NewtonsFormulas.html

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