Right triangle solver
Solve a right triangle from any two known sides, or a side and an acute angle.
A clear answer. Here’s how.
The right angle is at vertex C. With two sides, the third comes from Pythagoras (c² = a² + b²) and the angles from the arctangent. With one side and one acute angle, the other sides follow from sin, cos and tan, and the second angle is 90° minus the first. Also reports area (ab ÷ 2), perimeter, the altitude to the hypotenuse (ab ÷ c), the inradius ((a + b − c) ÷ 2) and the circumradius (c ÷ 2). Two angles alone cannot fix the size.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- First known value
- Side a (opposite angle A)
- First value
- 3
- Second known value
- Side b (opposite angle B)
- Second value
- 4
Example result
- Side a (opposite angle A)
- 3
- Side b (opposite angle B)
- 4
- Hypotenuse c
- 5
- Angle A (degrees)
- 36.86989765
- Angle B (degrees)
- 53.13010235
- Area
- 6
- Perimeter
- 12
- Altitude to the hypotenuse
- 2.4
- Inradius
- 1
- Circumradius
- 2.5
The right angle is at vertex C, so a and b are the legs and c is the hypotenuse. Uses Pythagoras and the sine, cosine and tangent definitions; the altitude is ab ÷ c, the inradius (a + b − c) ÷ 2 and the circumradius c ÷ 2. Lengths share one unit and areas use its square.