About the right triangle calculator
In a right triangle the two legs a and b meet at a 90° angle and the hypotenuse c is opposite it. The Pythagorean theorem a² + b² = c² links the sides, and the trigonometric ratios link sides to the acute angles α and β.
Two values are enough: two sides, a side and an angle, or even the area and the hypotenuse. If two triangles fit (for example area + hypotenuse, where the legs can be swapped), both are shown.
Formulas
| Pythagorean theorem | a² + b² = c² |
| Angles | sin α = a/c, cos α = b/c, tan α = a/b, α + β = 90° |
| Area | K = ab/2 |
| Height to hypotenuse | h = ab/c |
Frequently asked questions
How do I use the Pythagorean theorem?
For legs a and b, the hypotenuse is c = √(a² + b²). With legs 3 and 4 the hypotenuse is √25 = 5. To find a missing leg, use a = √(c² − b²).
How do I find an angle of a right triangle?
Use inverse trig: α = atan(a/b), or asin(a/c), or acos(b/c). The other acute angle is β = 90° − α.