# Triangle calculator VC

Please enter the coordinates of the three vertices

### Acute scalene triangle.

Sides: a = 9.22195444573   b = 3.60655512755   c = 8.6022325267

Area: T = 15.5
Perimeter: p = 21.42774209998
Semiperimeter: s = 10.71437104999

Angle ∠ A = α = 88.1522389734° = 88°9'9″ = 1.53985494444 rad
Angle ∠ B = β = 23.00988700828° = 23°32″ = 0.40215805401 rad
Angle ∠ C = γ = 68.83987401832° = 68°50'19″ = 1.20114626691 rad

Height: ha = 3.36224220962
Height: hb = 8.59878530415
Height: hc = 3.60436768011

Median: ma = 4.7176990566
Median: mb = 8.73221245983
Median: mc = 5.52326805086

Vertex coordinates: A[-2; 2] B[5; -3] C[-4; -1]
Centroid: CG[-0.33333333333; -0.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[3.40768495691; 1.44767443376]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 91.8487610266° = 91°50'51″ = 1.53985494444 rad
∠ B' = β' = 156.9911129917° = 156°59'28″ = 0.40215805401 rad
∠ C' = γ' = 111.1611259817° = 111°9'41″ = 1.20114626691 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    