Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 12.16655250606   b = 12.53299640861   c = 10.81766538264

Area: T = 60
Perimeter: p = 35.51221429731
Semiperimeter: s = 17.75660714866

Angle ∠ A = α = 62.30105271919° = 62°18'2″ = 1.08773493252 rad
Angle ∠ B = β = 65.7722254682° = 65°46'20″ = 1.14879424007 rad
Angle ∠ C = γ = 51.9277218126° = 51°55'38″ = 0.90663009277 rad

Height: ha = 9.86439392383
Height: hb = 9.57770426136
Height: hc = 11.09440039245

Median: ma = 10
Median: mb = 9.65766039579
Median: mc = 11.10218016556

Inradius: r = 3.37991258413
Circumradius: R = 6.87700891552

Vertex coordinates: A[1; 7] B[7; -2] C[-5; -4]
Centroid: CG[1; 0.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[1.52106066286; 3.37991258413]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 117.6999472808° = 117°41'58″ = 1.08773493252 rad
∠ B' = β' = 114.2287745318° = 114°13'40″ = 1.14879424007 rad
∠ C' = γ' = 128.0732781874° = 128°4'22″ = 0.90663009277 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     