Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 13.45436240471   b = 10.77703296143   c = 14.03656688476

Area: T = 68
Perimeter: p = 38.2659622509
Semiperimeter: s = 19.13298112545

Angle ∠ A = α = 64.11329737337° = 64°6'47″ = 1.11989824849 rad
Angle ∠ B = β = 46.07328292758° = 46°4'22″ = 0.80441225666 rad
Angle ∠ C = γ = 69.81441969905° = 69°48'51″ = 1.21884876021 rad

Height: ha = 10.1098800389
Height: hb = 12.6277282996
Height: hc = 9.69895987984

Median: ma = 10.54875115549
Median: mb = 12.64991106407
Median: mc = 9.96224294226

Inradius: r = 3.55546613135
Circumradius: R = 7.47770879842

Vertex coordinates: A[-9; -5] B[-8; 9] C[1; -1]
Centroid: CG[-5.33333333333; 1]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[3.42439752358; 3.55546613135]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 115.8877026266° = 115°53'13″ = 1.11989824849 rad
∠ B' = β' = 133.9277170724° = 133°55'38″ = 0.80441225666 rad
∠ C' = γ' = 110.1865803009° = 110°11'9″ = 1.21884876021 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     