Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 4.5832575695   b = 5.38551648071   c = 6.48107406984

Area: T = 12.17657956619
Perimeter: p = 16.44884812005
Semiperimeter: s = 8.22442406002

Angle ∠ A = α = 44.24772594687° = 44°14'50″ = 0.77222603627 rad
Angle ∠ B = β = 55.08108630005° = 55°4'51″ = 0.96113424142 rad
Angle ∠ C = γ = 80.67218775308° = 80°40'19″ = 1.40879898767 rad

Height: ha = 5.31439528826
Height: hb = 4.5221976986
Height: hc = 3.75875321182

Median: ma = 5.5
Median: mb = 4.92444289009
Median: mc = 3.80878865529

Inradius: r = 1.48804765879
Circumradius: R = 3.28437943339

Vertex coordinates: A[3; 0; 4] B[4; 5; 0] C[0; 4; 2]
Centroid: CG[2.33333333333; 3; 2]
Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.7532740531° = 135°45'10″ = 0.77222603627 rad
∠ B' = β' = 124.9199136999° = 124°55'9″ = 0.96113424142 rad
∠ C' = γ' = 99.32881224692° = 99°19'41″ = 1.40879898767 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     