Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 12.53299640861   b = 8.54440037453   c = 9.48768329805

Area: T = 40.5
Perimeter: p = 30.5610800812
Semiperimeter: s = 15.2880400406

Angle ∠ A = α = 87.87989036033° = 87°52'44″ = 1.53437762109 rad
Angle ∠ B = β = 42.95545915111° = 42°57'17″ = 0.75496990507 rad
Angle ∠ C = γ = 49.16765048855° = 49°9'59″ = 0.8588117392 rad

Height: ha = 6.46545037642
Height: hb = 9.48803329229
Height: hc = 8.53881496825

Median: ma = 6.5
Median: mb = 10.25991422643
Median: mc = 9.61876920308

Inradius: r = 2.65504541062
Circumradius: R = 6.26992775403

Vertex coordinates: A[5; 8; 0] B[-4; 11; 0] C[2; 0; 0]
Centroid: CG[1; 6.33333333333; 0]
Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 92.12110963967° = 92°7'16″ = 1.53437762109 rad
∠ B' = β' = 137.0455408489° = 137°2'43″ = 0.75496990507 rad
∠ C' = γ' = 130.8333495114° = 130°50'1″ = 0.8588117392 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     