Triangle Solver from Coordinates

Enter the (x, y) coordinates of three vertices to calculate all side lengths and interior angles. This free geometry calculator uses the distance formula and the law of cosines.

Triangle solver (vertex coordinates)

Input coordinates of points A, B, C. Decimals allowed.
🔹 Vertex coordinates
A
B
C
* all coordinates must be real numbers and points must not be collinear
—
—
—
— °
— °
— °

How the triangle is solved

Step 1: Distance between two points

The length of each side is found using the distance formula:

\[ AB=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2} \]

The same formula is applied to find \(BC\) and \(CA\).

Step 2: Find angles using the Law of Cosines

\[ A=\cos^{-1}\!\left(\frac{AB^2+AC^2-BC^2}{2\cdot AB\cdot AC}\right) \] \[ B=\cos^{-1}\!\left(\frac{AB^2+BC^2-CA^2}{2\cdot AB\cdot BC}\right) \] \[ C=\cos^{-1}\!\left(\frac{BC^2+CA^2-AB^2}{2\cdot BC\cdot CA}\right) \]

These formulas compute the three interior angles in degrees.

Educational notes

This calculator is useful for coordinate geometry, analytic geometry, and triangle problems involving vertices. It helps students visualize how algebra and geometry work together.

More Online Geometry Calculators