# Triangle calculator VC

Please enter the coordinates of the three vertices

### Acute scalene triangle.

Sides: a = 6.08327625303   b = 6.40331242374   c = 4.4722135955

Area: T = 13
Perimeter: p = 16.95880227227
Semiperimeter: s = 8.47990113614

Angle ∠ A = α = 65.22548594312° = 65°13'29″ = 1.13883885512 rad
Angle ∠ B = β = 72.89772710309° = 72°53'50″ = 1.27222973952 rad
Angle ∠ C = γ = 41.87878695379° = 41°52'40″ = 0.73109067072 rad

Height: ha = 4.27443736699
Height: hb = 4.06105178091
Height: hc = 5.81437767415

Median: ma = 4.61097722286
Median: mb = 4.27220018727
Median: mc = 5.83109518948

Vertex coordinates: A[2; 5] B[4; 1] C[-2; 0]
Centroid: CG[1.33333333333; 2]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[0.47217531124; 1.53331976154]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 114.7755140569° = 114°46'31″ = 1.13883885512 rad
∠ B' = β' = 107.1032728969° = 107°6'10″ = 1.27222973952 rad
∠ C' = γ' = 138.1222130462° = 138°7'20″ = 0.73109067072 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    