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[[Image:Triangle with notations 2.svg|thumb|198px|right||Figure 1 – A triangle. The angles ''α'', ''β'', and ''γ'' are respectively opposite the sides ''a'', ''b'', and ''c''.]]
{{Trigonometry}}
In [[trigonometry]], '''Mollweide's formula''', sometimes referred to in older texts as '''Mollweide's equations''',<ref>Ernest Julius Wilczynski, ''Plane Trigonometry and Applications'', Allyn and Bacon, 1914, page 102</ref> named after [[Karl Mollweide]], is a set of two relationships between sides and angles in a triangle.<ref>Michael Sullivan, ''Trigonometry'', Dellen Publishing Company, 1988, page 243.</ref> It can be used to check [[solution of triangles|solutions of triangles]].<ref>Ernest Julius Wilczynski, ''Plane Trigonometry and Applications'', Allyn and Bacon, 1914, page 105</ref>
Let ''a'', ''b'', and ''c'' be the lengths of the three sides of a triangle.
Let ''α'', ''β'', and ''γ'' be the measures of the angles opposite those three sides respectively. Mollweide's formula states that
Let a, b, and c be the lengths of the three sides of a triangle.
Let α, β, and γ be the measures of the angles opposite those three sides respectively. Mollweide's formula states that
and
Each of these identities uses all six parts of the triangle—the three angles and the lengths of the three sides.
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Additional reading
H. Arthur De Kleine, "Proof Without Words: Mollweide's Equation", Mathematics Magazine, volume 61, number 5, page 281, December, 1988.
↑Ernest Julius Wilczynski, Plane Trigonometry and Applications, Allyn and Bacon, 1914, page 102
