Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 9.11104335791   b = 8.6022325267   c = 4.5832575695

Area: T = 19.48107597388
Perimeter: p = 22.29553345411
Semiperimeter: s = 11.14876672706

Angle ∠ A = α = 81.2455333311° = 81°14'43″ = 1.41879985682 rad
Angle ∠ B = β = 68.94435313444° = 68°56'37″ = 1.20332916199 rad
Angle ∠ C = γ = 29.81111353446° = 29°48'40″ = 0.52203024655 rad

Height: ha = 4.27765823535
Height: hb = 4.52991846411
Height: hc = 8.50221005808

Median: ma = 5.17220402164
Median: mb = 5.78879184514
Median: mc = 8.55986213843

Inradius: r = 1.74875189442
Circumradius: R = 4.60989147162

Vertex coordinates: A[2; 3; 1] B[4; 7; 2] C[-5; 8; 1]
Centroid: CG[0.33333333333; 6; 1.33333333333]
Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 98.7554666689° = 98°45'17″ = 1.41879985682 rad
∠ B' = β' = 111.0566468656° = 111°3'23″ = 1.20332916199 rad
∠ C' = γ' = 150.1898864655° = 150°11'20″ = 0.52203024655 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     