Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 4.24326406871   b = 2.23660679775   c = 4.12331056256

Area: T = 4.5
Perimeter: p = 10.60218142902
Semiperimeter: s = 5.30109071451

Angle ∠ A = α = 77.47111922908° = 77°28'16″ = 1.35221273809 rad
Angle ∠ B = β = 30.96437565321° = 30°57'50″ = 0.54404195003 rad
Angle ∠ C = γ = 71.56550511771° = 71°33'54″ = 1.24990457724 rad

Height: ha = 2.12113203436
Height: hb = 4.02549223595
Height: hc = 2.18328206253

Median: ma = 2.55495097568
Median: mb = 4.03111288741
Median: mc = 2.69325824036

Inradius: r = 0.84989113046
Circumradius: R = 2.17330674684

Vertex coordinates: A[1; 4] B[5; 5] C[2; 2]
Centroid: CG[2.66766666667; 3.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[1.41548521743; 0.84989113046]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 102.5298807709° = 102°31'44″ = 1.35221273809 rad
∠ B' = β' = 149.0366243468° = 149°2'10″ = 0.54404195003 rad
∠ C' = γ' = 108.4354948823° = 108°26'6″ = 1.24990457724 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     