Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 8.06222577483   b = 11.4021754251   c = 11.18803398875

Area: T = 42.5
Perimeter: p = 30.64443518868
Semiperimeter: s = 15.32221759434

Angle ∠ A = α = 41.82201698801° = 41°49'13″ = 0.73298996582 rad
Angle ∠ B = β = 70.56599651718° = 70°33'36″ = 1.23215037123 rad
Angle ∠ C = γ = 67.6219864948° = 67°37'11″ = 1.18801892831 rad

Height: ha = 10.54329524401
Height: hb = 7.45549931641
Height: hc = 7.60326311235

Median: ma = 10.54875115549
Median: mb = 7.90656941504
Median: mc = 8.1399410298

Inradius: r = 2.77437574713
Circumradius: R = 6.04655308209

Vertex coordinates: A[-3; 2] B[7; -3] C[8; 5]
Centroid: CG[4; 1.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[0.97989732252; 2.77437574713]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.187983012° = 138°10'47″ = 0.73298996582 rad
∠ B' = β' = 109.4440034828° = 109°26'24″ = 1.23215037123 rad
∠ C' = γ' = 112.3880135052° = 112°22'49″ = 1.18801892831 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     