# 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

Inradius: r = 0.97703494294
Circumradius: R = 1.94545436483

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    