Right Triangle Solver

What Is the Right Triangle Solver?

Given the two legs of a right triangle, this tool solves for the hypotenuse (via the Pythagorean theorem) and both non-right angles (via inverse tangent).

How to Use This Tool

Enter both leg lengths. The hypotenuse and both angles appear instantly.

The Formulas

Worked Example

Which Angle Is Which

The tool labels the two legs Leg A and Leg B, and reports Angle A and Angle B. Angle A is the angle opposite Leg A, and Angle B is opposite Leg B. It computes Angle A as the inverse tangent of Leg A divided by Leg B, and then subtracts from 90 degrees to get Angle B. So a long Leg A relative to Leg B gives a large Angle A. Keeping this straight matters when you transfer the answer to a drawing or a real structure: the angle sits at the end of the hypotenuse that is farthest from the leg it faces.

A Second Worked Example

Take legs of 5 and 12. The hypotenuse is the square root of 25 + 144, which is the square root of 169, or 13. Angle A is the arctangent of 5 / 12, which is about 22.62 degrees, and Angle B is 90 minus that, about 67.38 degrees. The tool shows the hypotenuse to four decimal places and angles to two.

A non-integer case: legs 1 and 12 might describe a gentle ramp that rises 1 unit over 12 units of horizontal run. The hypotenuse is the square root of 145, about 12.0416, and the slope angle is about 4.76 degrees. Here Leg A is the rise and Leg B is the run.

Step-by-Step Tips

• Measure both legs in the same unit. The hypotenuse comes back in that unit, while angles are always in degrees.
• Make sure the two sides you measured are truly the legs and meet at the right angle. If one of your measurements is the slanted side, use the Pythagorean Theorem Calculator to solve for a missing leg instead.
• Check the result for sense: the hypotenuse must be longer than either leg, and the smaller angle must sit opposite the shorter leg.
• Round only at the end. If you copy a rounded hypotenuse into later calculations, small errors accumulate.

Requirements and Edge Cases

Both legs must be greater than zero, otherwise the tool shows a prompt asking for valid legs. Equal legs give a hypotenuse of leg times the square root of two and two angles of exactly 45 degrees. Very unequal legs push one angle close to 0 and the other close to 90. Because the angle uses an inverse tangent, you cannot use this tool if you know a leg and the hypotenuse; it needs both legs.

Common Mistakes

• Entering the hypotenuse as a leg. This gives a bigger triangle than you have and wrong angles.
• Swapping which leg is A and B and then reading the angles backwards.
• Mixing units, such as one leg in inches and the other in feet.
• Assuming the triangle is right-angled when it is not. The tool has no way to check this.

Practical Uses

Right triangles appear in roof pitch and stair layout, ladder placement, ramp design, surveying, screen diagonals and navigation. For carpentry or construction where safety codes apply, such as stair rise limits or ladder angles, confirm requirements with your local building authority rather than relying on a basic calculation. To work with angles in radians, follow up with the Degrees and Radians Converter.

Frequently Asked Questions