# 4 19 19 triangle

### Acute isosceles triangle.

Sides: a = 4   b = 19   c = 19

Area: T = 37.78988872554
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 12.08546568381° = 12°5'5″ = 0.21109170508 rad
Angle ∠ B = β = 83.95876715809° = 83°57'28″ = 1.46553378014 rad
Angle ∠ C = γ = 83.95876715809° = 83°57'28″ = 1.46553378014 rad

Height: ha = 18.89444436277
Height: hb = 3.97877776058
Height: hc = 3.97877776058

Median: ma = 18.89444436277
Median: mb = 9.91221138008
Median: mc = 9.91221138008

Inradius: r = 1.79994708217
Circumradius: R = 9.55330730387

Vertex coordinates: A[19; 0] B[0; 0] C[0.42110526316; 3.97877776058]
Centroid: CG[6.47436842105; 1.32659258686]
Coordinates of the circumscribed circle: U[9.5; 1.00655866356]
Coordinates of the inscribed circle: I[2; 1.79994708217]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.9155343162° = 167°54'55″ = 0.21109170508 rad
∠ B' = β' = 96.04223284191° = 96°2'32″ = 1.46553378014 rad
∠ C' = γ' = 96.04223284191° = 96°2'32″ = 1.46553378014 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    