# Triangle calculator VC

Please enter the coordinates of the three vertices

### Acute scalene triangle.

Sides: a = 19.64768827044   b = 11.04553610172   c = 20.88106130178

Area: T = 107
Perimeter: p = 51.57328567394
Semiperimeter: s = 25.78664283697

Angle ∠ A = α = 68.10663268583° = 68°6'23″ = 1.18986796451 rad
Angle ∠ B = β = 31.44328070705° = 31°26'34″ = 0.54987805094 rad
Angle ∠ C = γ = 80.45108660713° = 80°27'3″ = 1.4044132499 rad

Height: ha = 10.89223132092
Height: hb = 19.37546496531
Height: hc = 10.24987412519

Median: ma = 13.50992560861
Median: mb = 19.50664092031
Median: mc = 12.04215945788

Inradius: r = 4.14994695762
Circumradius: R = 10.58770031743

Vertex coordinates: A[-1; -3] B[5; 17] C[10; -2]
Centroid: CG[4.66766666667; 4]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[6.78765156621; 4.14994695762]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 111.8943673142° = 111°53'37″ = 1.18986796451 rad
∠ B' = β' = 148.557719293° = 148°33'26″ = 0.54987805094 rad
∠ C' = γ' = 99.54991339287° = 99°32'57″ = 1.4044132499 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    