Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 8.06222577483   b = 10.77703296143   c = 8.54440037453

Area: T = 34
Perimeter: p = 27.37765911079
Semiperimeter: s = 13.68882955539

Angle ∠ A = α = 47.64325452941° = 47°38'33″ = 0.83215192794 rad
Angle ∠ B = β = 80.81111639226° = 80°48'40″ = 1.41104208828 rad
Angle ∠ C = γ = 51.54662907833° = 51°32'47″ = 0.98996524914 rad

Height: ha = 8.43443619521
Height: hb = 6.3143641498
Height: hc = 7.95987980093

Median: ma = 8.84659030065
Median: mb = 6.32545553203
Median: mc = 8.5

Inradius: r = 2.48438738955
Circumradius: R = 5.45551688133

Vertex coordinates: A[-4; -1] B[-1; 7] C[6; 3]
Centroid: CG[0.33333333333; 3]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[0.40218031302; 2.48438738955]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.3577454706° = 132°21'27″ = 0.83215192794 rad
∠ B' = β' = 99.18988360774° = 99°11'20″ = 1.41104208828 rad
∠ C' = γ' = 128.4543709217° = 128°27'13″ = 0.98996524914 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     