Triangle calculator
For a right triangle, the hypotenuse is √(a² + b²) — a 3 and 4 give 5. For any triangle with three known sides, Heron’s formula gives the area from the semi-perimeter, and the cosine rule gives the angles.
How to solve a triangle
Heron formula is remarkable for needing no angle and no height: from the semi-perimeter s, the area is √(s(s−a)(s−b)(s−c)). It has been known for two thousand years and it is still the fastest route to the area of a triangle you have measured with a tape rather than drawn. The cosine rule then recovers every angle, so three tape measurements fully determine the shape.
Questions
Square both other sides, add them, take the square root. 3 and 4 give 5.
Area = √(s(s−a)(s−b)(s−c)), where s is half the perimeter. It needs only the three sides.
When any one is longer than the other two combined. The tool flags it.
Measure 3 along one edge and 4 along the other; the diagonal should be exactly 5. Any multiple works.
In plane geometry, yes. The three angles shown always sum to 180 degrees.