Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 12.80662484749   b = 14.14221356237   c = 7.21111025509

Area: T = 46
Perimeter: p = 34.15994866495
Semiperimeter: s = 17.08797433248

Angle ∠ A = α = 64.44400348282° = 64°26'24″ = 1.12546907779 rad
Angle ∠ B = β = 85.03302592719° = 85°1'49″ = 1.48440579881 rad
Angle ∠ C = γ = 30.53297058999° = 30°31'47″ = 0.53328438876 rad

Height: ha = 7.18439930469
Height: hb = 6.50553823869
Height: hc = 12.75881045132

Median: ma = 9.22195444573
Median: mb = 7.61657731059
Median: mc = 13

Inradius: r = 2.69332489046
Circumradius: R = 7.09877511814

Vertex coordinates: A[-4; 4] B[-10; 0] C[-2; -10]
Centroid: CG[-5.33333333333; -2]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[0.23441955569; 2.69332489046]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 115.5659965172° = 115°33'36″ = 1.12546907779 rad
∠ B' = β' = 94.97697407281° = 94°58'11″ = 1.48440579881 rad
∠ C' = γ' = 149.47702941° = 149°28'13″ = 0.53328438876 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     