The two laws
- Law of cosines: c² = a² + b² − 2ab·cos C. Use it with three sides, or two sides and the angle between them.
- Law of sines: a ÷ sin A = b ÷ sin B = c ÷ sin C. Use it with two angles and one side.
Side a is opposite angle A, side b opposite angle B and side c opposite angle C. The three angles always add up to 180°.
Example
A triangle with sides 5, 6 and 7 has angles of about 44.42°, 57.12° and 78.46°, an area of about 14.6969 (Heron’s formula) and a perimeter of 18.
For a right triangle, the Pythagorean theorem calculator is quicker.
Frequently asked questions
Why does it say the sides do not form a triangle?
Each side must be shorter than the sum of the other two. Sides 2, 3 and 6 cannot close a triangle.
How is the area calculated?
With Heron’s formula: √(s(s − a)(s − b)(s − c)), where s is half the perimeter.
What about two sides and an angle that is not between them (SSA)?
That case can have two different triangles, so it is not included. Use the law of sines and check both possibilities.
See also
Results are estimates for information only and are not financial, legal or medical advice. Rates, taxes and fees vary — confirm with a professional or your lender.