Triangle calculator VC

Please enter the coordinates of the three vertices

Obtuse scalene triangle.

Sides: a = 8.06222577483   b = 12.64991106407   c = 20.61655281281

Area: T = 10
Perimeter: p = 41.32768965171
Semiperimeter: s = 20.66334482585

Angle ∠ A = α = 4.3998705355° = 4°23'55″ = 0.07767718913 rad
Angle ∠ B = β = 6.9111227119° = 6°54'40″ = 0.12106236686 rad
Angle ∠ C = γ = 168.6990067526° = 168°41'24″ = 2.94441970937 rad

Height: ha = 2.48106946918
Height: hb = 1.58111388301
Height: hc = 0.97701425001

Median: ma = 16.62107701386
Median: mb = 14.31878210633
Median: mc = 2.5

Inradius: r = 0.48439463324
Circumradius: R = 52.55994901041

Vertex coordinates: A[-8; 1] B[12; 6] C[4; 5]
Centroid: CG[2.66766666667; 4]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[3.99325572425; 0.48439463324]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 175.6011294645° = 175°36'5″ = 0.07767718913 rad
∠ B' = β' = 173.0898772881° = 173°5'20″ = 0.12106236686 rad
∠ C' = γ' = 11.3109932474° = 11°18'36″ = 2.94441970937 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     