Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 6.40331242374   b = 5.38551648071   c = 3.74216573868

Area: T = 10.06223058987
Perimeter: p = 15.53299464313
Semiperimeter: s = 7.76549732157

Angle ∠ A = α = 87.15552896121° = 87°9'19″ = 1.52111467643 rad
Angle ∠ B = β = 57.13985427737° = 57°8'19″ = 0.99772557012 rad
Angle ∠ C = γ = 35.70661676141° = 35°42'22″ = 0.62331901881 rad

Height: ha = 3.1432936331
Height: hb = 3.73770465934
Height: hc = 5.3798528742

Median: ma = 3.35441019662
Median: mb = 4.5
Median: mc = 5.61224860802

Inradius: r = 1.29658584169
Circumradius: R = 3.20655122277

Vertex coordinates: A[1; 0; 1] B[-2; 1; 3] C[4; 2; 5]
Centroid: CG[1; 1; 3]
Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 92.84547103879° = 92°50'41″ = 1.52111467643 rad
∠ B' = β' = 122.8611457226° = 122°51'41″ = 0.99772557012 rad
∠ C' = γ' = 144.2943832386° = 144°17'38″ = 0.62331901881 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     