Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 5.38551648071   b = 7.07110678119   c = 6.40331242374

Area: T = 16.5
Perimeter: p = 18.85993568564
Semiperimeter: s = 9.43296784282

Angle ∠ A = α = 46.79899106082° = 46°47'24″ = 0.81766379968 rad
Angle ∠ B = β = 73.14216012323° = 73°8'30″ = 1.27765617617 rad
Angle ∠ C = γ = 60.06884881595° = 60°4'7″ = 1.04883928951 rad

Height: ha = 6.12879461598
Height: hb = 4.66769047558
Height: hc = 5.15437341423

Median: ma = 6.18546584384
Median: mb = 4.74334164903
Median: mc = 5.40883269132

Inradius: r = 1.75497945583
Circumradius: R = 3.6944298588

Vertex coordinates: A[1; 3] B[5; -2] C[0; -4]
Centroid: CG[2; -1]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[0.53302407752; 1.75497945583]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.2110089392° = 133°12'36″ = 0.81766379968 rad
∠ B' = β' = 106.8588398768° = 106°51'30″ = 1.27765617617 rad
∠ C' = γ' = 119.9321511841° = 119°55'53″ = 1.04883928951 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     