# 14 19 22 triangle

### Acute scalene triangle.

Sides: a = 14   b = 19   c = 22

Area: T = 131.7421935237
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 39.07655206502° = 39°4'32″ = 0.68219964923 rad
Angle ∠ B = β = 58.81113776665° = 58°48'41″ = 1.02664521779 rad
Angle ∠ C = γ = 82.11331016833° = 82°6'47″ = 1.43331439834 rad

Height: ha = 18.82202764624
Height: hb = 13.86875721302
Height: hc = 11.9776539567

Median: ma = 19.32661480901
Median: mb = 15.80334806293
Median: mc = 12.5549900398

Inradius: r = 4.79106158268
Circumradius: R = 11.10550440952

Vertex coordinates: A[22; 0] B[0; 0] C[7.25; 11.9776539567]
Centroid: CG[9.75; 3.99221798557]
Coordinates of the circumscribed circle: U[11; 1.52438124416]
Coordinates of the inscribed circle: I[8.5; 4.79106158268]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.924447935° = 140°55'28″ = 0.68219964923 rad
∠ B' = β' = 121.1898622333° = 121°11'19″ = 1.02664521779 rad
∠ C' = γ' = 97.88768983167° = 97°53'13″ = 1.43331439834 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    