How to use it
- Enter two of the three sides: leg a, leg b or the hypotenuse c.
- Leave the side you want to find empty.
- Read the missing side and the calculation that produced it.
The theorem
In a right triangle, a² + b² = c², where c is the hypotenuse, the side opposite the right angle and always the longest side.
Finding a missing side
For the hypotenuse, c = √(a² + b²). For a leg, a = √(c² − b²). With a hypotenuse of 13 and a leg of 5, the other leg is √(169 − 25) = √144 = 12.
A real-life example
A 10-foot ladder stands with its foot 6 feet from a wall. It reaches √(10² − 6²) = √64 = 8 feet up the wall.
Pythagorean triples
Some right triangles have whole-number sides: 3-4-5, 5-12-13, 8-15-17 and 7-24-25. Any multiple also works, such as 6-8-10.
Frequently asked questions
Which side is the hypotenuse?
The longest side, opposite the right angle.
Does the theorem work for every triangle?
No, only for right triangles. For other triangles, use the law of cosines in the Triangle Calculator.
How do I check if a triangle is a right triangle?
Check whether the squares of the two shorter sides add up to the square of the longest side.
Why must the hypotenuse be longest?
Because c² = a² + b², c² is larger than either a² or b², so c is larger than both legs.