How this calculator works
Side classification depends on equal lengths: three equal sides are equilateral, exactly two are labelled isosceles here, and three different sides are scalene. Angle classification uses the largest angle. For side measurements, the law of cosines gives the angles. Two angles determine the third and the side proportions, but do not determine size. Equality is compared with a relative tolerance of 1 in 10 billion to accommodate rounding.
Formula
A + B + C = 180°; cos C = (a² + b² - c²)/(2ab). A largest angle below, equal to or above 90° gives an acute, right or obtuse triangle.
Worked example
Sides 3, 4 and 5 give a scalene right triangle. Angles 40° and 40° leave 100°, so the triangle is isosceles and obtuse.
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Frequently asked questions
Can an equilateral triangle be right?
No. All of its angles are 60°, so it is acute.
Why are two angles enough?
The angle sum supplies the third angle. Equal angles also identify equal opposite sides.
Can I use a non-included angle with two sides?
Use the law of sines calculator for that case. It can have two possible triangles, whereas the included-angle case here is unique.