Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 7.81102496759   b = 8.54440037453   c = 4.24326406871

Area: T = 16.5
Perimeter: p = 20.59768941083
Semiperimeter: s = 10.29884470542

Angle ∠ A = α = 65.55660452196° = 65°33'22″ = 1.14441688337 rad
Angle ∠ B = β = 84.80655710923° = 84°48'20″ = 1.48801364396 rad
Angle ∠ C = γ = 29.63883836882° = 29°38'18″ = 0.51772873803 rad

Height: ha = 4.22552170378
Height: hb = 3.86223578575
Height: hc = 7.77881745931

Median: ma = 5.5
Median: mb = 4.61097722286
Median: mc = 7.90656941504

Inradius: r = 1.60221833111
Circumradius: R = 4.298961845

Vertex coordinates: A[-2; 2] B[1; 5] C[6; -1]
Centroid: CG[1.66766666667; 2]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[0.14656530283; 1.60221833111]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 114.444395478° = 114°26'38″ = 1.14441688337 rad
∠ B' = β' = 95.19444289077° = 95°11'40″ = 1.48801364396 rad
∠ C' = γ' = 150.3621616312° = 150°21'42″ = 0.51772873803 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     