# 8 13 19 triangle

### Obtuse scalene triangle.

Sides: a = 8   b = 13   c = 19

Area: T = 40.98878030638
Perimeter: p = 40
Semiperimeter: s = 20

Angle ∠ A = α = 19.38332300516° = 19°23' = 0.33883011841 rad
Angle ∠ B = β = 32.63768975036° = 32°38'13″ = 0.57696213191 rad
Angle ∠ C = γ = 127.9879872445° = 127°58'48″ = 2.23436701504 rad

Height: ha = 10.2476950766
Height: hb = 6.3065815856
Height: hc = 4.31545055857

Median: ma = 15.78797338381
Median: mb = 13.04879883507
Median: mc = 5.1233475383

Inradius: r = 2.04993901532
Circumradius: R = 12.05223659009

Vertex coordinates: A[19; 0] B[0; 0] C[6.73768421053; 4.31545055857]
Centroid: CG[8.57989473684; 1.43881685286]
Coordinates of the circumscribed circle: U[9.5; -7.41768405544]
Coordinates of the inscribed circle: I[7; 2.04993901532]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.6176769948° = 160°37' = 0.33883011841 rad
∠ B' = β' = 147.3633102496° = 147°21'47″ = 0.57696213191 rad
∠ C' = γ' = 52.02201275551° = 52°1'12″ = 2.23436701504 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    