The Pythagorean Theorem: Formula, Triples and Examples
Use a² + b² = c² to find a hypotenuse or a missing leg, learn the common triples, and avoid the mistake of adding instead of squaring.
The theorem
- a² + b² = c²
- c is the hypotenuse
- a and b are the legs
It only works on right triangles. The hypotenuse is opposite the right angle.
Triples worth knowing
- 3, 4, 5
- 5, 12, 13
- 8, 15, 17
Multiples count too: 6, 8, 10 is just 3, 4, 5 doubled.
Example 1
Legs are 6 and 8. Find the hypotenuse.
- c² = 6² + 8² = 36 + 64
- c² = 100, so c = 10
c = 10
Example 2
Hypotenuse is 13 and one leg is 5. Find the other leg.
- Subtract: b² = 13² − 5² = 169 − 25
- b² = 144, so b = 12
b = 12
Common mistake
c = a + b
Square each leg first, then add, then take the square root.
The hypotenuse is always the longest side. If you get a shorter one, recheck.
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