Find the missing side of a right triangle using a² + b² = c², where c is the hypotenuse.
Enter all three sides to check if they form a right triangle.
| Property | Value |
|---|---|
| Leg a | 3 |
| Leg b | 4 |
| Hypotenuse c | 5 |
| Angle A | 36.86989765° |
| Angle B | 53.13010235° |
| Angle C | 90° |
| Perimeter | 12 |
| Area | 6 |
| a | b | c |
|---|---|---|
| 3 | 4 | 5 |
| 5 | 12 | 13 |
| 8 | 15 | 17 |
| 7 | 24 | 25 |
| 20 | 21 | 29 |
| 9 | 40 | 41 |
| 11 | 60 | 61 |
| 28 | 45 | 53 |
| 33 | 56 | 65 |
| 36 | 77 | 85 |
You have a 12-foot ladder and need to know how far up the wall it reaches if you set its foot 3 feet out. Eyeballing it will not do, because the height is not simply 12 minus 3. This calculator solves for any one missing side of a right triangle, and a second panel tests whether three numbers form a right triangle at all.
The theorem says the squares of the two legs add up to the square of the hypotenuse: a² + b² = c². To find c, take c = √(a² + b²). To find a leg, take √(c² − other leg²). The page has a tab for each: Find c, Find b and Find a.
What changes if the foot of the ladder moves? Keep the ladder at 12 and slide the foot outward. At 3 ft the reach is 11.61895004 ft. At 4 ft it is 11.3137085. At 6 ft it is 10.39230485, and at 9 ft just 7.93725393. The first foot of movement costs only about 0.3 ft of height, but going from 6 to 9 ft costs about 2.45 ft. The relationship curves, so small adjustments near the wall matter far less than the same adjustments far out.
Worked example with the Find a tab: set leg b = 3 and hypotenuse c = 12. Then a = √(12² − 3²) = √(144 − 9) = √135 = 11.61895004. The page also reports angle A = 75.52248781° (the angle at the foot of the ladder), area 17.42842506 and perimeter 26.61895004. Everything is rounded to eight decimals.
Probably the c box has a shorter side in it. Entering a = 5, b = 3 and c = 4 compares 25 + 9 = 34 against 16 and reports that it is not a right triangle. The checker expects c to be the hypotenuse.
It is a right triangle, and the label is a little loose. Strictly, a Pythagorean triple has whole numbers, but the check works for any numbers whose squares match within 0.000001.
In Find a or Find b, c must be strictly larger than the known leg. If c equals the leg, the other leg would be zero, and if it is smaller, no triangle exists. The page shows an error rather than a number.
Using 6 and 8 for the legs, the diagonal should be exactly 10. If it reads 10 ft and half an inch (10.0417 ft), the corner is about 90.5° rather than 90°. A small error in the diagonal turns into a visible error in the corner.
Only for right triangles. For other triangles, c² = a² + b² − 2ab·cos C is the general version, and the triangle calculator on this site uses it. The two agree when C = 90°, because cos 90° = 0.
No, √2 is irrational and runs on forever. The page rounds to eight decimals, so 1.41421356 is shown. For a length that feels exact, do not treat the rounded figure as a perfect value.