🔺 Triangle Calculator
Enter any 2 values (sides a, b, or hypotenuse c).
Triangle Formulas
Heron's Formula: Area = √[s(s−a)(s−b)(s−c)] where s = (a+b+c)/2
Law of Cosines: c² = a² + b² − 2ab·cos(C)
Pythagorean Theorem: a² + b² = c²
Frequently Asked Questions
The law of cosines generalizes the Pythagorean theorem to any triangle: c² = a² + b² − 2ab·cos(C). It's used to find a side when two sides and the included angle are known, or to find an angle when all three sides are known.
Heron's formula calculates triangle area from three side lengths without needing the height: Area = √[s(s−a)(s−b)(s−c)], where s = (a+b+c)/2 is the semi-perimeter. It works for any triangle.
For right triangles only: a² + b² = c², where c is the hypotenuse (longest side, opposite the right angle). Example: a=3, b=4 → c = √(9+16) = √25 = 5. The 3-4-5 triangle is the most famous Pythagorean triple.
No. The triangle inequality theorem states that the sum of any two sides must be greater than the third side. If a=1, b=2, c=10: 1+2=3, which is not greater than 10, so no triangle is possible.