Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 7.28801098893   b = 7.61657731059   c = 6.40331242374

Area: T = 21.5
Perimeter: p = 21.29990072326
Semiperimeter: s = 10.65495036163

Angle ∠ A = α = 61.85883987677° = 61°51'30″ = 1.08796327285 rad
Angle ∠ B = β = 67.28655876468° = 67°17'8″ = 1.17443550436 rad
Angle ∠ C = γ = 50.85660135854° = 50°51'22″ = 0.88876048815 rad

Height: ha = 5.90765042498
Height: hb = 5.6466176613
Height: hc = 6.71554717612

Median: ma = 6.02107972894
Median: mb = 5.70108771255
Median: mc = 6.72768120235

Inradius: r = 2.019887344
Circumradius: R = 4.12880543701

Vertex coordinates: A[-4; -1] B[1; 3] C[3; -4]
Centroid: CG[0; -0.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[0.84551098121; 2.019887344]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 118.1421601232° = 118°8'30″ = 1.08796327285 rad
∠ B' = β' = 112.7144412353° = 112°42'52″ = 1.17443550436 rad
∠ C' = γ' = 129.1443986415° = 129°8'38″ = 0.88876048815 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     