13 19 23 triangle

Acute scalene triangle.

Sides: a = 13   b = 19   c = 23

Area: T = 123.5499746963
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 34.4177308278° = 34°25'2″ = 0.60106953491 rad
Angle ∠ B = β = 55.69986751605° = 55°41'55″ = 0.97221252705 rad
Angle ∠ C = γ = 89.88440165614° = 89°53'2″ = 1.56987720339 rad

Height: ha = 198.9999610713
Height: hb = 132.9999733646
Height: hc = 10.73991084316

Median: ma = 20.06986322404
Median: mb = 16.08657079421
Median: mc = 11.52217186218

Vertex coordinates: A[23; 0] B[0; 0] C[7.32660869565; 10.73991084316]
Centroid: CG[10.10986956522; 3.58797028105]
Coordinates of the circumscribed circle: U[11.5; 0.02332793999]
Coordinates of the inscribed circle: I[8.5; 4.49108998896]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.5832691722° = 145°34'58″ = 0.60106953491 rad
∠ B' = β' = 124.3011324839° = 124°18'5″ = 0.97221252705 rad
∠ C' = γ' = 90.11659834386° = 90°6'58″ = 1.56987720339 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    