# 19 20 23 triangle

### Acute scalene triangle.

Sides: a = 19   b = 20   c = 23

Area: T = 180.9310926046
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 51.87441170479° = 51°52'27″ = 0.90553741391 rad
Angle ∠ B = β = 55.98998797635° = 55°54' = 0.97656369533 rad
Angle ∠ C = γ = 72.22660031886° = 72°13'34″ = 1.26105815612 rad

Height: ha = 19.04553606365
Height: hb = 18.09330926046
Height: hc = 15.7333124004

Median: ma = 19.34655421222
Median: mb = 18.5744175621
Median: mc = 15.75659512566

Inradius: r = 5.83664814854
Circumradius: R = 12.07664318613

Vertex coordinates: A[23; 0] B[0; 0] C[10.6522173913; 15.7333124004]
Centroid: CG[11.21773913043; 5.2444374668]
Coordinates of the circumscribed circle: U[11.5; 3.68664897261]
Coordinates of the inscribed circle: I[11; 5.83664814854]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.1265882952° = 128°7'33″ = 0.90553741391 rad
∠ B' = β' = 124.1100120236° = 124°6' = 0.97656369533 rad
∠ C' = γ' = 107.7743996811° = 107°46'26″ = 1.26105815612 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    