- Area
- 6 square units
- Perimeter
- 12
- Side a
- 3
- Side b
- 4
- Side c
- 5
- Angle A
- 36.87 °
- Angle B
- 53.13 °
- Angle C
- 90 °
- Semiperimeter
- 6
- Altitude to a
- 4
- Altitude to b
- 3
- Altitude to c
- 2.4
- Median from A
- 4.27
- Median from B
- 3.61
- Median from C
- 2.5
- Inradius
- 1
- Circumradius
- 2.5
- Vertex A
- (0, 0)
- Vertex B
- (5, 0)
- Vertex C
- (3.2, 2.4)
- Centroid
- (2.73, 0.8)
- Incenter
- (3, 1)
- Circumcenter
- (2.5, 0)
How it works
The hypotenuse altitude is a separate length
In a 3–4–5 right triangle, the altitude to the hypotenuse is 2.4, while the legs are 3 and 4. Select the altitude field only for that perpendicular segment; substituting a leg changes the problem.
Solving a right triangle from known quantities
Choose the pair of known quantities supported by the mode, such as two sides or a side and an acute angle. Label the hypotenuse and legs carefully before entering values. The right-angle assumption supplies information that a general triangle problem does not have. Review the resulting side lengths and angle units together to check that the solution matches the diagram you intended.
Two legs: formula and assumptions
c = √(a²+b²); area = ab/2; angle A = atan(a/b).
The right angle is between the two entered legs.
Any two known quantities: formula and assumptions
a=c sin(A); b=c cos(A); h=ab/c; area=ab/2; perimeter=a+b+c.
Enter the first and second values in the order shown. Angles use degrees; lengths use a shared unit and area uses its square. Multiple labeled solutions are displayed when applicable. Angular inputs can use degrees or radians. Calculated angles are shown in degrees.
Worked example
Using the Two legs example:
- Leg a
- 3
- Leg b
- 4
c = √(a²+b²); area = ab/2; angle A = atan(a/b).
Example result
Area: 6 square units
Perimeter: 12
Side a: 3
Side b: 4
Side c: 5
Angle A: 36.87 °
Angle B: 53.13 °
Angle C: 90 °
Semiperimeter: 6
Altitude to a: 4
Altitude to b: 3
Altitude to c: 2.4
Median from A: 4.27
Median from B: 3.61
Median from C: 2.5
Inradius: 1
Circumradius: 2.5
Vertex A: (0, 0)
Vertex B: (5, 0)
Vertex C: (3.2, 2.4)
Centroid: (2.73, 0.8)
Incenter: (3, 1)
Circumcenter: (2.5, 0)
These are illustrative inputs. Change the values to explore a different scenario.
Formula references
References explain the underlying methods; they do not imply endorsement or individual professional review of Finflo.
Common questions
Why can a known pair produce more than one solution?
Some measurements do not distinguish the two labeled legs or angles. The solver displays each admissible labeled solution.
Can I enter angles in radians?
Yes. Select radians for angular inputs. Calculated angles are displayed in degrees, and all lengths must follow the stated unit convention.
Prepared by Finflo. See our methodology and editorial policy.