Triangle calculator VC

Please enter the coordinates of the three vertices

Right scalene triangle.

Sides: a = 12.80662484749   b = 19.20993727123   c = 23.08767927612

Area: T = 123
Perimeter: p = 55.10224139484
Semiperimeter: s = 27.55112069742

Angle ∠ A = α = 33.6990067526° = 33°41'24″ = 0.58880026035 rad
Angle ∠ B = β = 56.3109932474° = 56°18'36″ = 0.98327937232 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 19.20993727123
Height: hb = 12.80662484749
Height: hc = 10.65554428129

Median: ma = 20.24884567313
Median: mb = 16.00878105936
Median: mc = 11.54333963806

Inradius: r = 4.4644414213
Circumradius: R = 11.54333963806

Vertex coordinates: A[4; 11] B[2; -12] C[-8; -4]
Centroid: CG[-0.66766666667; -1.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[2.9766276142; 4.4644414213]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.3109932474° = 146°18'36″ = 0.58880026035 rad
∠ B' = β' = 123.6990067526° = 123°41'24″ = 0.98327937232 rad
∠ C' = γ' = 90° = 1.57107963268 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     