Triangle Calculator

How to Solve a Right Triangle

A right triangle has one 90° angle. If you know the two shorter sides (legs a and b), you can find the hypotenuse and both acute angles.

Finding the hypotenuse (Pythagorean theorem)

c = √(a² + b²)

1. Square both legs: a² and b²
2. Add them together
3. Take the square root

Finding the angles

Use inverse tangent: Angle A = arctan(a ÷ b) and Angle B = arctan(b ÷ a). The two acute angles always add to 90°.

Worked example

For sides a = 3, b = 4: c = √(9 + 16) = √25 = 5. Angle A = arctan(3/4) ≈ 36.87°. Angle B = arctan(4/3) ≈ 53.13°. Check: 36.87 + 53.13 + 90 = 180°.

Real-world uses

Construction (roof pitch, stair angles), navigation, surveying, and physics problems involving vectors.