Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 4.12331056256   b = 5.38551648071   c = 6.32545553203

Area: T = 11
Perimeter: p = 15.83328257531
Semiperimeter: s = 7.91664128765

Angle ∠ A = α = 40.23663583093° = 40°14'11″ = 0.70222569315 rad
Angle ∠ B = β = 57.52988077092° = 57°31'44″ = 1.00440671093 rad
Angle ∠ C = γ = 82.23548339816° = 82°14'5″ = 1.43552686128 rad

Height: ha = 5.33657837508
Height: hb = 4.08552974399
Height: hc = 3.47985054262

Median: ma = 5.5
Median: mb = 4.61097722286
Median: mc = 3.60655512755

Inradius: r = 1.3989518229
Circumradius: R = 3.19215435785

Vertex coordinates: A[5; -1] B[-1; 1] C[0; -3]
Centroid: CG[1.33333333333; -1]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[0.8844238873; 1.3989518229]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.7643641691° = 139°45'49″ = 0.70222569315 rad
∠ B' = β' = 122.4711192291° = 122°28'16″ = 1.00440671093 rad
∠ C' = γ' = 97.76551660184° = 97°45'55″ = 1.43552686128 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     