Find the hypotenuse of a right triangle from its two shorter sides with Pythagoras's theorem, plus its area, perimeter, angles and height.
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With side a (leg) 3, side b (leg) 4, the hypotenuse (c) is 5.
| Side a (leg) | 3 |
|---|---|
| Side b (leg) | 4 |
| Hypotenuse (c) | 5 |
|---|---|
| Area | 6 |
| Perimeter | 12 |
| Angle A (opposite side a) | 36.86989765 ° |
| Angle B (opposite side b) | 53.13010235 ° |
| Height to the hypotenuse | 2.4 |
In a right triangle the two sides that meet at the right angle are called legs, and the longest side, opposite the right angle, is the hypotenuse. Pythagoras's theorem says the square on the hypotenuse equals the sum of the squares on the legs. Enter both legs to get the hypotenuse, the two acute angles and the height from the right angle to the hypotenuse.
c = √(a² + b²) (Pythagoras's theorem). Area = a × b ÷ 2. Angle A = arctan(a ÷ b). In a right triangle the two sides that meet at the right angle are called legs, and the longest side, opposite the right angle, is the hypotenuse. Pythagoras's theorem says the square on the hypotenuse equals the sum of the squares on the legs. Enter both legs to get the hypotenuse, the two acute angles and the height from the right angle to the hypotenuse.
With side a (leg) 3, side b (leg) 4, the hypotenuse (c) is 5. Area: 6; Perimeter: 12; Angle A (opposite side a): 36.86989765 °; Angle B (opposite side b): 53.13010235 °; Height to the hypotenuse: 2.4.
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Square each leg, add the squares and take the square root. With legs 5 and 12: 25 + 144 = 169, and √169 = 13.
Rearrange the theorem: leg = √(hypotenuse² − other leg²). For a hypotenuse of 10 and a leg of 6, the missing leg is √(100 − 36) = 8. You can check the answer by entering 6 and 8 here.
Whole-number sides that satisfy a² + b² = c², such as 3-4-5, 5-12-13 and 8-15-17. Multiplying a triple by any number gives another right triangle, so 6-8-10 is also right-angled.