Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 7.07110678119   b = 11.4021754251   c = 12.64991106407

Area: T = 40
Perimeter: p = 31.12219327035
Semiperimeter: s = 15.56109663518

Angle ∠ A = α = 33.6990067526° = 33°41'24″ = 0.58880026035 rad
Angle ∠ B = β = 63.43549488229° = 63°26'6″ = 1.10771487178 rad
Angle ∠ C = γ = 82.87549836511° = 82°52'30″ = 1.44664413322 rad

Height: ha = 11.3143708499
Height: hb = 7.01664641545
Height: hc = 6.32545553203

Median: ma = 11.51108644332
Median: mb = 8.5154693183
Median: mc = 7.07110678119

Inradius: r = 2.57105344447
Circumradius: R = 6.3743774392

Vertex coordinates: A[3; 7] B[-1; -5] C[6; -4]
Centroid: CG[2.66766666667; -0.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[1.28552672223; 2.57105344447]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.3109932474° = 146°18'36″ = 0.58880026035 rad
∠ B' = β' = 116.5655051177° = 116°33'54″ = 1.10771487178 rad
∠ C' = γ' = 97.12550163489° = 97°7'30″ = 1.44664413322 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     