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Mollweide's formula
Relation between sides and angles of a triangle / From Wikipedia, the free encyclopedia
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In trigonometry, Mollweide's formula is a pair of relationships between sides and angles in a triangle.[1][2]
![](http://upload.wikimedia.org/wikipedia/commons/thumb/4/49/Triangle_with_notations_2.svg/198px-Triangle_with_notations_2.svg.png)
A variant in more geometrical style was first published by Isaac Newton in 1707 and then by Friedrich Wilhelm von Oppel [de] in 1746. Thomas Simpson published the now-standard expression in 1748. Karl Mollweide republished the same result in 1808 without citing those predecessors.[3]
It can be used to check the consistency of solutions of triangles.[4]
Let
and
be the lengths of the three sides of a triangle.
Let
and
be the measures of the angles opposite those three sides respectively. Mollweide's formulas are