# 13 18 19 triangle

### Acute scalene triangle.

Sides: a = 13   b = 18   c = 19

Area: T = 112.2549721603
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 41.02882543699° = 41°1'42″ = 0.71660781251 rad
Angle ∠ B = β = 65.35444154842° = 65°21'16″ = 1.14106497309 rad
Angle ∠ C = γ = 73.61773301459° = 73°37'2″ = 1.28548647976 rad

Height: ha = 17.2699187939
Height: hb = 12.47221912892
Height: hc = 11.81657601688

Median: ma = 17.32877234512
Median: mb = 13.56546599663
Median: mc = 12.5

Inradius: r = 4.49899888641
Circumradius: R = 9.90220290129

Vertex coordinates: A[19; 0] B[0; 0] C[5.42110526316; 11.81657601688]
Centroid: CG[8.14403508772; 3.93985867229]
Coordinates of the circumscribed circle: U[9.5; 2.7932879978]
Coordinates of the inscribed circle: I[7; 4.49899888641]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.972174563° = 138°58'18″ = 0.71660781251 rad
∠ B' = β' = 114.6465584516° = 114°38'44″ = 1.14106497309 rad
∠ C' = γ' = 106.3832669854° = 106°22'58″ = 1.28548647976 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    