# Triangle calculator VC

Please enter the coordinates of the three vertices

### Acute scalene triangle.

Sides: a = 10.05498756211   b = 9.22195444573   c = 7.21111025509

Area: T = 32
Perimeter: p = 26.48105226293
Semiperimeter: s = 13.24402613147

Angle ∠ A = α = 74.2911362171° = 74°17'29″ = 1.29766288757 rad
Angle ∠ B = β = 62.02105256115° = 62°1'14″ = 1.08224623757 rad
Angle ∠ C = γ = 43.68881122175° = 43°41'17″ = 0.76325014022 rad

Height: ha = 6.36882380173
Height: hb = 6.94217746502
Height: hc = 8.87552031396

Median: ma = 6.5766473219
Median: mb = 7.43330343737
Median: mc = 8.944427191

Vertex coordinates: A[2; 5] B[6; -1] C[-4; -2]
Centroid: CG[1.33333333333; 0.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[1.28439625741; 2.41768707278]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 105.7098637829° = 105°42'31″ = 1.29766288757 rad
∠ B' = β' = 117.9799474388° = 117°58'46″ = 1.08224623757 rad
∠ C' = γ' = 136.3121887783° = 136°18'43″ = 0.76325014022 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    