# 13 22 27 triangle

### Obtuse scalene triangle.

Sides: a = 13   b = 22   c = 27

Area: T = 141.7322141732
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 28.50435101171° = 28°30'13″ = 0.49774800999 rad
Angle ∠ B = β = 53.86111853369° = 53°51'40″ = 0.94400550232 rad
Angle ∠ C = γ = 97.63553045461° = 97°38'7″ = 1.70440575305 rad

Height: ha = 21.80549448819
Height: hb = 12.88547401575
Height: hc = 10.49986771653

Median: ma = 23.75439470404
Median: mb = 18.11107702763
Median: mc = 12.01104121495

Inradius: r = 4.5722004572
Circumradius: R = 13.62107636208

Vertex coordinates: A[27; 0] B[0; 0] C[7.66766666667; 10.49986771653]
Centroid: CG[11.55655555556; 3.54995590551]
Coordinates of the circumscribed circle: U[13.5; -1.81097518098]
Coordinates of the inscribed circle: I[9; 4.5722004572]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.4966489883° = 151°29'47″ = 0.49774800999 rad
∠ B' = β' = 126.1398814663° = 126°8'20″ = 0.94400550232 rad
∠ C' = γ' = 82.36546954539° = 82°21'53″ = 1.70440575305 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    