Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 5.83109518948   b = 6.08327625303   c = 2.23660679775

Area: T = 6.5
Perimeter: p = 14.15497824026
Semiperimeter: s = 7.07548912013

Angle ∠ A = α = 72.89772710309° = 72°53'50″ = 1.27222973952 rad
Angle ∠ B = β = 85.6011294645° = 85°36'5″ = 1.49440244355 rad
Angle ∠ C = γ = 21.5011434324° = 21°30'5″ = 0.37552708229 rad

Height: ha = 2.22994816069
Height: hb = 2.1377186835
Height: hc = 5.81437767415

Median: ma = 3.53655339059
Median: mb = 3.20215621187
Median: mc = 5.85223499554

Inradius: r = 0.91987420435
Circumradius: R = 3.05503661629

Vertex coordinates: A[3; 1] B[2; -1] C[-3; 2]
Centroid: CG[0.66766666667; 0.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[0.07106724649; 0.91987420435]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 107.1032728969° = 107°6'10″ = 1.27222973952 rad
∠ B' = β' = 94.3998705355° = 94°23'55″ = 1.49440244355 rad
∠ C' = γ' = 158.4998565676° = 158°29'55″ = 0.37552708229 rad

How did we calculate this triangle?

1. We compute side a from coordinates using the Pythagorean theorem 2. We compute side b from coordinates using the Pythagorean theorem 3. We compute side c from coordinates using the Pythagorean theorem Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS. 4. The triangle circumference is the sum of the lengths of its three sides 5. Semiperimeter of the triangle 6. The triangle area using Heron's formula 7. Calculate the heights of the triangle from its area. 8. Calculation of the inner angles of the triangle using a Law of Cosines     