Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 21.88329842572   b = 31.28549948058   c = 31.95992693909

Area: T = 324.4687779417
Perimeter: p = 85.12772484539
Semiperimeter: s = 42.56436242269

Angle ∠ A = α = 40.46989435811° = 40°28'8″ = 0.70663163103 rad
Angle ∠ B = β = 68.10988116358° = 68°6'32″ = 1.18987230127 rad
Angle ∠ C = γ = 71.42222447831° = 71°25'20″ = 1.24765533306 rad

Height: ha = 29.65548017038
Height: hb = 20.74327094958
Height: hc = 20.30550811612

Median: ma = 29.6710804674
Median: mb = 22.48220422782
Median: mc = 21.75991182036

Inradius: r = 7.62331238601
Circumradius: R = 16.85880722083

Vertex coordinates: A[-30.75; -3.56; 64.62] B[-6.75; -19.74; 51.07] C[-5.7; 1.66; 46.62]
Centroid: CG[-14.4; -7.21333333333; 54.10333333333]
Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.5311056419° = 139°31'52″ = 0.70663163103 rad
∠ B' = β' = 111.8911188364° = 111°53'28″ = 1.18987230127 rad
∠ C' = γ' = 108.5787755217° = 108°34'40″ = 1.24765533306 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     