Newton's formulas relate the side lengths and opposite angles of a triangle. Let a triangle
have side lengths 
,
, and 
with opposite angles 
, 
, and 
. Then
 |  | ![(cos[1/2(B-C)])/(sin(1/2A))](/images/equations/NewtonsFormulas/Inline9.svg) |
(1)
|
 |  | ![(cos[1/2(C-A)])/(sin(1/2B))](/images/equations/NewtonsFormulas/Inline12.svg) |
(2)
|
 |  | ![(cos[1/2(A-B)])/(sin(1/2C)).](/images/equations/NewtonsFormulas/Inline15.svg) |
(3)
|
Newton's Formulas
See also
Mollweide's Formulas, TriangleExplore with Wolfram|Alpha
References
Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 146, 1987.Referenced on Wolfram|Alpha
Newton's FormulasCite this as:
Weisstein, Eric W. "Newton's Formulas." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NewtonsFormulas.html