# 19 19 19 triangle

### Equilateral triangle.

Sides: a = 19   b = 19   c = 19

Area: T = 156.3187585383
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 60° = 1.04771975512 rad
Angle ∠ B = β = 60° = 1.04771975512 rad
Angle ∠ C = γ = 60° = 1.04771975512 rad

Height: ha = 16.45444826719
Height: hb = 16.45444826719
Height: hc = 16.45444826719

Median: ma = 16.45444826719
Median: mb = 16.45444826719
Median: mc = 16.45444826719

Inradius: r = 5.48548275573
Circumradius: R = 10.97696551146

Vertex coordinates: A[19; 0] B[0; 0] C[9.5; 16.45444826719]
Centroid: CG[9.5; 5.48548275573]
Coordinates of the circumscribed circle: U[9.5; 5.48548275573]
Coordinates of the inscribed circle: I[9.5; 5.48548275573]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120° = 1.04771975512 rad
∠ B' = β' = 120° = 1.04771975512 rad
∠ C' = γ' = 120° = 1.04771975512 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    