A triangle is fixed once you know enough about it, and three sides are always enough - there is exactly one triangle with those lengths, up to turning it around. That is why the three-sides mode can find every angle without being told any of them, and why builders trust a triangle to hold its shape when a rectangle will not.

Using it in three steps

1. 1 Choose the mode that matches what you know: two sides of a right triangle, or all three sides of any triangle.
2. 2 Type the lengths you have. In right-triangle mode, leave the unknown one blank rather than guessing at it.
3. 3 Read the results next to the drawing. The picture is drawn from the numbers, so a wrong entry shows up as a wrong shape.

The triangle inequality

Sides of 1, 2 and 9 cannot close into a triangle: the short two together are shorter than the long one, so they never meet. This calculator checks that before doing anything else. Without the check, the law of cosines quietly returns nothing usable and the page would show an empty result with no explanation.

Why the drawing is to scale

The shape you see is built from the sides you entered, not from a stock picture with numbers pasted beside it. If you mistype a length, the triangle visibly changes, and a very flat or very lopsided drawing is often the first sign that a measurement is wrong. A generic illustration would hide exactly that.