Right Triangle Calculator
Solve a right triangle from two sides. Get the hypotenuse or missing leg, both acute angles, and the area.
Independently verified for accuracy
Calculator by Toolsloft ↗- Hypotenuse
- 5
- Legs
- 3 and 4
- Angles
- 36.869898° and 53.130102°
- Area
- 6
Solve a right triangle from two known sides. Give the two legs to find the hypotenuse, or give one leg and the hypotenuse to find the other leg. The tool returns every side, both acute angles, and the area. Good for geometry class and quick layout math.
How this is calculated
Sides use the Pythagorean theorem: the hypotenuse is the square root of the sum of the squares of the legs, and a missing leg is the square root of the hypotenuse squared minus the known leg squared. Each acute angle comes from the arctangent of the opposite over adjacent side, and the area is half the product of the two legs.
How to use
- Choose whether you know two legs or a leg and the hypotenuse.
- Enter the two known sides.
- Read every side, both acute angles, and the area.
Examples
- Two legs:
legs 3 and 4 give a hypotenuse of 5 - Leg and hypotenuse:
leg 6, hypotenuse 10 gives the other leg 8
FAQ
- What is the Pythagorean theorem?
- In a right triangle the square of the hypotenuse equals the sum of the squares of the two legs, so the hypotenuse is the square root of leg a squared plus leg b squared.
- How are the angles found?
- Each acute angle is the arctangent of the side opposite it divided by the side next to it. The two acute angles always add up to 90 degrees.
- Why must the hypotenuse be longer than the leg?
- The hypotenuse is always the longest side of a right triangle. If the entered hypotenuse is not longer than the leg, the triangle cannot exist.