# 12 17 20 triangle

### Acute scalene triangle.

Sides: a = 12   b = 17   c = 20

Area: T = 101.6665812838
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 36.7299236457° = 36°43'45″ = 0.64110461079 rad
Angle ∠ B = β = 57.91100487437° = 57°54'36″ = 1.01107210206 rad
Angle ∠ C = γ = 85.36107147993° = 85°21'39″ = 1.49898255251 rad

Height: ha = 16.94443021397
Height: hb = 11.96106838633
Height: hc = 10.16765812838

Median: ma = 17.56441680703
Median: mb = 14.13332940251
Median: mc = 10.79435165725

Inradius: r = 4.15496250138
Circumradius: R = 10.03328711445

Vertex coordinates: A[20; 0] B[0; 0] C[6.375; 10.16765812838]
Centroid: CG[8.79216666667; 3.38988604279]
Coordinates of the circumscribed circle: U[10; 0.81114822249]
Coordinates of the inscribed circle: I[7.5; 4.15496250138]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.2710763543° = 143°16'15″ = 0.64110461079 rad
∠ B' = β' = 122.0989951256° = 122°5'24″ = 1.01107210206 rad
∠ C' = γ' = 94.63992852007° = 94°38'21″ = 1.49898255251 rad

# How did we calculate this triangle?

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. ### 1. The triangle circumference is the sum of the lengths of its three sides ### 2. Semiperimeter of the triangle ### 3. The triangle area using Heron's formula ### 4. Calculate the heights of the triangle from its area. ### 5. Calculation of the inner angles of the triangle using a Law of Cosines    