Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 11.3143708499   b = 12.16655250606   c = 7.21111025509

Area: T = 40
Perimeter: p = 30.69903361105
Semiperimeter: s = 15.34551680553

Angle ∠ A = α = 65.7722254682° = 65°46'20″ = 1.14879424007 rad
Angle ∠ B = β = 78.6990067526° = 78°41'24″ = 1.37334007669 rad
Angle ∠ C = γ = 35.5387677792° = 35°32'16″ = 0.6220249486 rad

Height: ha = 7.07110678119
Height: hb = 6.57659594922
Height: hc = 11.09440039245

Median: ma = 8.24662112512
Median: mb = 7.28801098893
Median: mc = 11.18803398875

Inradius: r = 2.60766837363
Circumradius: R = 6.20332249677

Vertex coordinates: A[7; 4] B[3; -2] C[-5; 6]
Centroid: CG[1.66766666667; 2.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[0.52113367473; 2.60766837363]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 114.2287745318° = 114°13'40″ = 1.14879424007 rad
∠ B' = β' = 101.3109932474° = 101°18'36″ = 1.37334007669 rad
∠ C' = γ' = 144.4622322208° = 144°27'44″ = 0.6220249486 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     