# 11 19 19 triangle

### Acute isosceles triangle.

Sides: a = 11   b = 19   c = 19

Area: T = 100.0265934137
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 33.65328977855° = 33°39'10″ = 0.58773538692 rad
Angle ∠ B = β = 73.17435511073° = 73°10'25″ = 1.27771193922 rad
Angle ∠ C = γ = 73.17435511073° = 73°10'25″ = 1.27771193922 rad

Height: ha = 18.18765334795
Height: hb = 10.52990456986
Height: hc = 10.52990456986

Median: ma = 18.18765334795
Median: mb = 12.27880291578
Median: mc = 12.27880291578

Inradius: r = 4.08326911893
Circumradius: R = 9.92549260561

Vertex coordinates: A[19; 0] B[0; 0] C[3.18442105263; 10.52990456986]
Centroid: CG[7.39547368421; 3.51096818995]
Coordinates of the circumscribed circle: U[9.5; 2.8733004911]
Coordinates of the inscribed circle: I[5.5; 4.08326911893]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.3477102215° = 146°20'50″ = 0.58773538692 rad
∠ B' = β' = 106.8266448893° = 106°49'35″ = 1.27771193922 rad
∠ C' = γ' = 106.8266448893° = 106°49'35″ = 1.27771193922 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    