# Triangle calculator VC

Please enter the coordinates of the three vertices

### Acute scalene triangle.

Sides: a = 9.22195444573   b = 6.08327625303   c = 8.944427191

Area: T = 26
Perimeter: p = 24.24765788976
Semiperimeter: s = 12.12332894488

Angle ∠ A = α = 72.89772710309° = 72°53'50″ = 1.27222973952 rad
Angle ∠ B = β = 39.09438588862° = 39°5'38″ = 0.68223165549 rad
Angle ∠ C = γ = 68.00988700828° = 68°32″ = 1.18769787035 rad

Height: ha = 5.64401919033
Height: hb = 8.54987473399
Height: hc = 5.81437767415

Median: ma = 6.10332778079
Median: mb = 8.55986213843
Median: mc = 6.40331242374

Vertex coordinates: A[-1; -3] B[3; 5] C[5; -4]
Centroid: CG[2.33333333333; -0.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[2.64395476356; 2.14546324539]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 107.1032728969° = 107°6'10″ = 1.27222973952 rad
∠ B' = β' = 140.9066141114° = 140°54'22″ = 0.68223165549 rad
∠ C' = γ' = 111.9911129917° = 111°59'28″ = 1.18769787035 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    