Formula and method
For a right triangle, a²+b²=c², where c is the hypotenuse opposite the 90° angle. To find c, use √(a²+b²). To find a leg, subtract the other leg’s square from c² before taking the square root.
Worked example
With a = 3 and b = 4, c = √(9+16) = 5. The area is 3 × 4 / 2 = 6 square units and perimeter is 12 units. A = atan(3/4) ≈ 36.86989765° and B ≈ 53.13010235°.
Inputs and limitations
This theorem applies only to right triangles. For a general triangle use the Triangle Calculator. The hypotenuse must be longer than either leg. Convert all side measurements to the same unit first; the area is in that unit squared.
Whole-number right triangles
Each row satisfies a²+b²=c². Multiplying all three sides by the same positive factor preserves the right angle.
| Leg a | Leg b | Hypotenuse c |
|---|---|---|
| 3 | 4 | 5 |
| 5 | 12 | 13 |
| 8 | 15 | 17 |
| 7 | 24 | 25 |
| 20 | 21 | 29 |