# 12 13 20 triangle

### Obtuse scalene triangle.

Sides: a = 12   b = 13   c = 20

Area: T = 74.90661913329
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 35.18438154883° = 35°11'2″ = 0.61440734237 rad
Angle ∠ B = β = 38.62548328731° = 38°37'29″ = 0.67441305067 rad
Angle ∠ C = γ = 106.1911351639° = 106°11'29″ = 1.85333887232 rad

Height: ha = 12.48443652221
Height: hb = 11.52440294358
Height: hc = 7.49106191333

Median: ma = 15.76438827704
Median: mb = 15.15875063912
Median: mc = 7.51766481892

Inradius: r = 3.32991640592
Circumradius: R = 10.41330244259

Vertex coordinates: A[20; 0] B[0; 0] C[9.375; 7.49106191333]
Centroid: CG[9.79216666667; 2.49768730444]
Coordinates of the circumscribed circle: U[10; -2.90436318111]
Coordinates of the inscribed circle: I[9.5; 3.32991640592]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.8166184512° = 144°48'58″ = 0.61440734237 rad
∠ B' = β' = 141.3755167127° = 141°22'31″ = 0.67441305067 rad
∠ C' = γ' = 73.80986483614° = 73°48'31″ = 1.85333887232 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    