# 10 13 19 triangle

### Obtuse scalene triangle.

Sides: a = 10   b = 13   c = 19

Area: T = 60.79547366143
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 29.49895673359° = 29°29'22″ = 0.5154690045 rad
Angle ∠ B = β = 39.78876882825° = 39°47'16″ = 0.69444261623 rad
Angle ∠ C = γ = 110.7232744382° = 110°43'22″ = 1.93224764463 rad

Height: ha = 12.15989473229
Height: hb = 9.35330364022
Height: hc = 6.39994459594

Median: ma = 15.49219333848
Median: mb = 13.7220422734
Median: mc = 6.65220673478

Inradius: r = 2.89549874578
Circumradius: R = 10.15771292909

Vertex coordinates: A[19; 0] B[0; 0] C[7.68442105263; 6.39994459594]
Centroid: CG[8.89547368421; 2.13331486531]
Coordinates of the circumscribed circle: U[9.5; -3.59440611337]
Coordinates of the inscribed circle: I[8; 2.89549874578]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.5110432664° = 150°30'38″ = 0.5154690045 rad
∠ B' = β' = 140.2122311717° = 140°12'44″ = 0.69444261623 rad
∠ C' = γ' = 69.27772556184° = 69°16'38″ = 1.93224764463 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    