# Triangle calculator VC

Please enter the coordinates of the three vertices

### Acute scalene triangle.

Sides: a = 13.45436240471   b = 10.77703296143   c = 14.03656688476

Area: T = 68
Perimeter: p = 38.2659622509
Semiperimeter: s = 19.13298112545

Angle ∠ A = α = 64.11329737337° = 64°6'47″ = 1.11989824849 rad
Angle ∠ B = β = 46.07328292758° = 46°4'22″ = 0.80441225666 rad
Angle ∠ C = γ = 69.81441969905° = 69°48'51″ = 1.21884876021 rad

Height: ha = 10.1098800389
Height: hb = 12.6277282996
Height: hc = 9.69895987984

Median: ma = 10.54875115549
Median: mb = 12.64991106407
Median: mc = 9.96224294226

Inradius: r = 3.55546613135
Circumradius: R = 7.47770879842

Vertex coordinates: A[-9; -5] B[-8; 9] C[1; -1]
Centroid: CG[-5.33333333333; 1]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[3.42439752358; 3.55546613135]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 115.8877026266° = 115°53'13″ = 1.11989824849 rad
∠ B' = β' = 133.9277170724° = 133°55'38″ = 0.80441225666 rad
∠ C' = γ' = 110.1865803009° = 110°11'9″ = 1.21884876021 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    