The Right Triangle Calculator finds all sides, angles, height, area and perimeter of a right triangle from any two values, at least one of them a side.
| a | 3 |
| b | 4 |
| c (hypotenuse) | 5 |
| ∠α | 36.869898° = 0.643501 rad |
| ∠β | 53.130102° = 0.927295 rad |
| Height h (to hypotenuse) | 2.4 |
| Area | 6 |
| Perimeter | 12 |
A right triangle has one 90° angle. The side opposite it is the hypotenuse c; the other sides are legs a and b. Angle α is opposite a and β is opposite b, and α + β = 90°.
sin α = a/c, cos α = b/c, tan α = a/b. Knowing one side and one angle, or two sides, is enough to find everything else.
Worked example (defaults): a = 3, c = 5 gives b = 4, α = 36.87°, β = 53.13°, area 6, perimeter 12 and height to the hypotenuse 2.4.
A 45°-45°-90° triangle has sides in the ratio 1 : 1 : √2. A 30°-60°-90° triangle has sides 1 : √3 : 2. These appear often in geometry and design.
What is the height h? The perpendicular from the right angle to the hypotenuse, h = ab/c.
Can I use radians? Yes, choose radian for the angle unit.
Why do I need at least one side? Angles alone fix the shape, not the size.