# 13 19 22 triangle

### Acute scalene triangle.

Sides: a = 13   b = 19   c = 22

Area: T = 122.9633409192
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 36.03994162329° = 36°2'22″ = 0.62990064738 rad
Angle ∠ B = β = 59.30435587083° = 59°18'13″ = 1.03550423576 rad
Angle ∠ C = γ = 84.65770250587° = 84°39'25″ = 1.47875438222 rad

Height: ha = 18.91774475679
Height: hb = 12.9443516757
Height: hc = 11.17884917447

Median: ma = 19.5
Median: mb = 15.37704261489
Median: mc = 12

Inradius: r = 4.55442003404
Circumradius: R = 11.04880020758

Vertex coordinates: A[22; 0] B[0; 0] C[6.63663636364; 11.17884917447]
Centroid: CG[9.54554545455; 3.72661639149]
Coordinates of the circumscribed circle: U[11; 1.02987613269]
Coordinates of the inscribed circle: I[8; 4.55442003404]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.9610583767° = 143°57'38″ = 0.62990064738 rad
∠ B' = β' = 120.6966441292° = 120°41'47″ = 1.03550423576 rad
∠ C' = γ' = 95.34329749413° = 95°20'35″ = 1.47875438222 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    