# 6 19 19 triangle

### Acute isosceles triangle.

Sides: a = 6   b = 19   c = 19

Area: T = 56.28549891179
Perimeter: p = 44
Semiperimeter: s = 22

Angle ∠ A = α = 18.16994405748° = 18°10'10″ = 0.31771165613 rad
Angle ∠ B = β = 80.91552797126° = 80°54'55″ = 1.41222380462 rad
Angle ∠ C = γ = 80.91552797126° = 80°54'55″ = 1.41222380462 rad

Height: ha = 18.76216630393
Height: hb = 5.92547356966
Height: hc = 5.92547356966

Median: ma = 18.76216630393
Median: mb = 10.40443260233
Median: mc = 10.40443260233

Inradius: r = 2.55884085963
Circumradius: R = 9.62106823255

Vertex coordinates: A[19; 0] B[0; 0] C[0.94773684211; 5.92547356966]
Centroid: CG[6.6499122807; 1.97549118989]
Coordinates of the circumscribed circle: U[9.5; 1.5199055104]
Coordinates of the inscribed circle: I[3; 2.55884085963]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.8310559425° = 161°49'50″ = 0.31771165613 rad
∠ B' = β' = 99.08547202874° = 99°5'5″ = 1.41222380462 rad
∠ C' = γ' = 99.08547202874° = 99°5'5″ = 1.41222380462 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    