Solve a right triangle from any two values.
Give any two values. With legs 3 and 4 the hypotenuse is c = 5, the angles are 36.87° and 53.13°, and the area is 6.
A right triangle has one 90° angle. Enter any two of the five values — leg a, leg b, hypotenuse c, angle A or angle B — and the calculator solves the rest, together with the area, perimeter, altitude to the hypotenuse, inradius, circumradius and the sine, cosine and tangent of angle A.
It combines the Pythagorean theorem with basic trigonometry (SOH-CAH-TOA). For the theorem alone see the Pythagorean Theorem Calculator; for any triangle use the Triangle Calculator; for angles in practice see the Slope Calculator.
The calculator applies the standard method step by step.
| Item | Value |
|---|---|
| Leg a | 3 |
| Leg b | 4 |
| Hypotenuse c | 5 |
| Angle A | 36.8698976458° |
| Angle B | 53.1301023542° |
| Angle C | 90° |
| Area (½ab) | 6 |
| Perimeter | 12 |
| Altitude to the hypotenuse (ab ÷ c) | 2.4 |
| Inradius ((a + b − c) ÷ 2) | 1 |
| Circumradius (c ÷ 2) | 2.5 |
| sin A, cos A, tan A | 0.6, 0.8, 0.75 |
| Given | Hypotenuse |
|---|---|
| Legs 3 and 4 | c = 5 |
| Leg 5, hypotenuse 13 | c = 13 |
| Hypotenuse 10, A = 30° | c = 10 |
| Leg 6, A = 45° | c = 8.4852813742 |
| Legs 8 and 15 | c = 17 |
Use the Pythagorean theorem for missing sides and the trig ratios (sin, cos, tan) for angles.
Sin = Opposite ÷ Hypotenuse, Cos = Adjacent ÷ Hypotenuse, Tan = Opposite ÷ Adjacent.
A right triangle whose sides are in the ratio 1 : √3 : 2.
An isosceles right triangle whose sides are in the ratio 1 : 1 : √2.
Two: either two sides, or one side and one acute angle. Two angles alone are not enough.
The side opposite the right angle and the longest side of the triangle.
It uses the standard method: c² = a² + b² sin A = a ÷ c cos A = b ÷ c tan A = a ÷ b The full working and a worked example are shown on this page.
Decimal results use standard double-precision arithmetic (about 15–16 significant digits). Tools that work with whole numbers — big numbers, factors, bases, combinations — use exact integer arithmetic, so no digits are lost.
Yes for checking your work and learning the method. The steps and formula are shown so you can understand the answer, but follow your teacher's rules about calculators in exams.
No. Everything is calculated in your browser and nothing you enter is uploaded or saved.
