Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 4.12331056256   b = 5.09990195136   c = 6.40331242374

Area: T = 10.5
Perimeter: p = 15.62552493766
Semiperimeter: s = 7.81326246883

Angle ∠ A = α = 40.03302592719° = 40°1'49″ = 0.69986598247 rad
Angle ∠ B = β = 52.6966051722° = 52°41'46″ = 0.92197196054 rad
Angle ∠ C = γ = 87.27436890061° = 87°16'25″ = 1.52332132235 rad

Height: ha = 5.09332481258
Height: hb = 4.11884388379
Height: hc = 3.28796489997

Median: ma = 5.40883269132
Median: mb = 4.74334164903
Median: mc = 3.35441019662

Inradius: r = 1.344397855
Circumradius: R = 3.20551899523

Vertex coordinates: A[1; 1] B[5; 6] C[6; 2]
Centroid: CG[4; 3]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[1.02439836571; 1.344397855]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.9769740728° = 139°58'11″ = 0.69986598247 rad
∠ B' = β' = 127.3043948278° = 127°18'14″ = 0.92197196054 rad
∠ C' = γ' = 92.72663109939° = 92°43'35″ = 1.52332132235 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     