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Figure 1 – A triangle. The angles α, β, and γ are respectively opposite the sides a, b, and c.

Template:Trigonometry In trigonometry, Mollweide's formula, sometimes referred to in older texts as Mollweide's equations, named after Karl Mollweide, is a set of two relationships between sides and angles in a triangle. It can be used to check solutions of triangles.

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

$\frac{a+b}{c}=\frac{\cos \left(\frac{\alpha -\beta }{2}\right)}{\sin \left(\frac{\gamma }{2}\right)}$

and

$\frac{a-b}{c}=\frac{\sin \left(\frac{\alpha -\beta }{2}\right)}{\cos \left(\frac{\gamma }{2}\right)}.$

Each of these identities uses all six parts of the triangle—the three angles and the lengths of the three sides.

See also

• Law of sines
• Law of cosines
• Law of tangents
• Law of cotangents

References

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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.