- 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
An angle label determines the SSA case
For a = 10, b = 12 and A = 30°, A must be opposite side a. Entering an angle between a and b instead describes SAS; the same three numbers can therefore represent a different triangle problem.
Choosing a triangle-solving case
Three sides, two sides with an included angle, and two angles with a side provide different starting information. Select the matching case rather than placing an unrelated measurement in an available field. A side-side-angle problem can have ambiguous solutions, which is why the selected method matters. Check whether the entered values can form a triangle before interpreting its area or angles.
Three sides: formula and assumptions
s = (a+b+c)/2; area = √[s(s−a)(s−b)(s−c)].
The sum of any two sides must exceed the third. Angles are calculated from normalized side geometry. Altitudes, medians, radii and centers are also shown in coordinates A=(0,0), B=(c,0), with C above the x-axis.
Two sides & included angle: formula and assumptions
c² = a²+b²−2ab cos(C); area = ab sin(C)/2.
The angle must lie strictly between 0° and 180°. Angular inputs can use degrees or radians. Calculated angles are shown in degrees.
Two angles & side: formula and assumptions
a/sin(A) = b/sin(B) = c/sin(C), with C = 180°−A−B.
The sum of the given angles must be less than 180°. Angular inputs can use degrees or radians. Calculated angles are shown in degrees.
Two sides & a non-included angle: formula and assumptions
sin(B)=b sin(A)/a. Both B and 180°−B must be checked.
SSA can give no triangle, one triangle, or two triangles. Solutions with nonpositive remaining angles are excluded. Angular inputs can use degrees or radians. Calculated angles are shown in degrees.
Worked example
Using the Three sides example:
- Side a
- 3
- Side b
- 4
- Side c
- 5
s = (a+b+c)/2; area = √[s(s−a)(s−b)(s−c)].
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 the SSA case have two triangles?
A non-included angle can match two supplementary angle candidates. Only candidates with valid positive remaining angles form solutions.
What condition must three side lengths satisfy?
Every side must be shorter than the sum of the other two. Equality would form a degenerate straight-line shape.
Prepared by Finflo. See our methodology and editorial policy.