Triangle calculator VC

Please enter the coordinates of the three vertices

Acute isosceles triangle.

Sides: a = 3.46441016151   b = 3.31766247904   c = 3.31766247904

Area: T = 4.89989794856
Perimeter: p = 10.09773511958
Semiperimeter: s = 5.04986755979

Angle ∠ A = α = 62.96443082106° = 62°57'52″ = 1.09989344895 rad
Angle ∠ B = β = 58.51878458947° = 58°31'4″ = 1.0211329082 rad
Angle ∠ C = γ = 58.51878458947° = 58°31'4″ = 1.0211329082 rad

Height: ha = 2.82884271247
Height: hb = 2.95441957835
Height: hc = 2.95441957835

Median: ma = 2.82884271247
Median: mb = 2.95880398915
Median: mc = 2.95880398915

Vertex coordinates: A[1; -1; 2] B[2; 0; -1] C[0; 2; 1]
Centroid: CG[1; 0.33333333333; 0.66766666667]
Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 117.0365691789° = 117°2'8″ = 1.09989344895 rad
∠ B' = β' = 121.4822154105° = 121°28'56″ = 1.0211329082 rad
∠ C' = γ' = 121.4822154105° = 121°28'56″ = 1.0211329082 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    