# 19 19 23 triangle

### Acute isosceles triangle.

Sides: a = 19   b = 19   c = 23

Area: T = 173.9321559816
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 52.75222191042° = 52°45'8″ = 0.92106999111 rad
Angle ∠ B = β = 52.75222191042° = 52°45'8″ = 0.92106999111 rad
Angle ∠ C = γ = 74.49655617917° = 74°29'44″ = 1.33001928314 rad

Height: ha = 18.30985852438
Height: hb = 18.30985852438
Height: hc = 15.12444834623

Median: ma = 18.83548082018
Median: mb = 18.83548082018
Median: mc = 15.12444834623

Inradius: r = 5.70326740923
Circumradius: R = 11.93442918686

Vertex coordinates: A[23; 0] B[0; 0] C[11.5; 15.12444834623]
Centroid: CG[11.5; 5.04114944874]
Coordinates of the circumscribed circle: U[11.5; 3.19901915937]
Coordinates of the inscribed circle: I[11.5; 5.70326740923]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.2487780896° = 127°14'52″ = 0.92106999111 rad
∠ B' = β' = 127.2487780896° = 127°14'52″ = 0.92106999111 rad
∠ C' = γ' = 105.5044438208° = 105°30'16″ = 1.33001928314 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    