Solve right triangles by finding sides, perimeter, area, and angles
Triangular Dimension Visual (scaled)
Step-by-Step Solver
Evidence-based guide
The Pythagorean Theorem is a fundamental principle in geometry stating that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Given two legs (a and b), calculate the hypotenuse: c = √(a² + b²).
Given the hypotenuse (c) and one leg (a), calculate the other leg: b = √(c² − a²).
In addition to side lengths, the solver computes the area, perimeter, and all interior angles of the right triangle (which sum to 180 degrees).
The theorem applies strictly to Euclidean flat-plane geometry and right-angled triangles (where one angle is exactly 90 degrees).
A Pythagorean triple consists of three positive integers (a, b, c) that satisfy the equation a² + b² = c² (e.g. 3, 4, 5 or 5, 12, 13).
We use inverse trigonometric functions: α = arcsin(a/c) and β = arcsin(b/c).
No. The hypotenuse is always the longest side of a right triangle. If a leg is entered as greater than or equal to the hypotenuse, a validation error is thrown.
