Geometry
Finding the hypotenuse
Square each leg, add, then take the square root. The result must exceed both inputs.
The Formula
c = sqrt(a^2 + b^2)
Square each leg, add, then take the square root. The result must exceed both inputs.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| a | One leg adjacent to the right angle | — | Any positive length, in the same unit as b. |
| b | The other leg adjacent to the right angle | — | Order does not affect the result. |
| c | Hypotenuse | same as the legs | Always the longest side of the triangle. |
What Each Symbol Means
a
One leg adjacent to the right angle
Any positive length, in the same unit as b.
b
The other leg adjacent to the right angle
Order does not affect the result.
csame as the legs
Hypotenuse
Always the longest side of the triangle.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to use the pythagorean theorem page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Use The Pythagorean Theorem, filed under Math. Every number the guide produces comes from substituting into this one line.