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Calculate the missing side of a right triangle using a² + b² = c². Enter any two sides to find the third, plus area and perimeter. Includes Pythagorean triples reference.
The Pythagorean theorem states that in a right-angled triangle, a² + b² = c², where c is the hypotenuse and a, b are the other two sides. It is one of the most fundamental theorems in Euclidean geometry.
Hypotenuse (c)
5.000000
Side a
3.0000
Side b
4.0000
Hypotenuse c
5.0000
Area (½ × a × b)
6.0000
Perimeter (a + b + c)
12.0000
Verification
3.00² + 4.00² = 9.00 + 16.00 = 25.00
5.00² = 25.00 ✓
| a | b | c |
|---|---|---|
| 3 | 4 | 5 |
| 5 | 12 | 13 |
| 8 | 15 | 17 |
| 7 | 24 | 25 |
| 9 | 40 | 41 |
| 11 | 60 | 61 |
| 6 | 8 | 10 |
| 20 | 21 | 29 |
Formula
a² + b² = c²a = Length of one leg of the right triangle
b = Length of the other leg of the right triangle
c = Length of the hypotenuse (longest side, opposite the right angle)
Worked Example
Find the hypotenuse when a = 5 and b = 12
Did you know? Although named after the Greek mathematician Pythagoras (~570–495 BC), the theorem was known to Babylonian mathematicians over 1,000 years earlier, as evidenced by the clay tablet Plimpton 322 (~1800 BC) which lists Pythagorean triples (source: British Museum / Yale Babylonian Collection).
Sources
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