How it works
Three side lengths fix a triangle completely. The angles come from the law of cosines and the area from Heron's formula, which needs only the sides.
The sides must satisfy the triangle inequality: the two shorter sides together must be longer than the longest side, or they will not meet.
The calculator also classifies the triangle by its angles (acute, right, obtuse) and sides (scalene, isosceles, equilateral), and gives the height to each side and the radii of the inscribed and circumscribed circles.
Formula
cos A = (b² + c² − a²) ÷ 2bc; Area = √(s(s − a)(s − b)(s − c)), s = (a + b + c) ÷ 2
Questions people ask
What is Heron's formula?
A way to find a triangle's area from its three sides. Compute the semi-perimeter s = (a + b + c)/2, then area = √(s(s−a)(s−b)(s−c)). For 3-4-5, s = 6 and area = √(6·3·2·1) = 6.
How can I tell if a triangle is right, acute or obtuse from its sides?
Compare the square of the longest side with the sum of the squares of the other two. Equal means right, larger means obtuse, smaller means acute.
Why do the angles always add to 180°?
It is a property of flat (Euclidean) geometry. The calculator computes two angles with the law of cosines and the third as 180° minus the others.