# 11 21 27 triangle

### Obtuse scalene triangle.

Sides: a = 11   b = 21   c = 27

Area: T = 107.6990238648
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 22.32549954181° = 22°19'30″ = 0.39896446755 rad
Angle ∠ B = β = 46.4844388962° = 46°29'4″ = 0.81113056382 rad
Angle ∠ C = γ = 111.191061562° = 111°11'26″ = 1.94106423399 rad

Height: ha = 19.58800433905
Height: hb = 10.25662132045
Height: hc = 7.97770547146

Median: ma = 23.55331314266
Median: mb = 17.74111949992
Median: mc = 9.93773034572

Inradius: r = 3.65105165643
Circumradius: R = 14.47990281792

Vertex coordinates: A[27; 0] B[0; 0] C[7.57440740741; 7.97770547146]
Centroid: CG[11.5254691358; 2.65990182382]
Coordinates of the circumscribed circle: U[13.5; -5.23437612682]
Coordinates of the inscribed circle: I[8.5; 3.65105165643]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.6755004582° = 157°40'30″ = 0.39896446755 rad
∠ B' = β' = 133.5165611038° = 133°30'56″ = 0.81113056382 rad
∠ C' = γ' = 68.80993843802° = 68°48'34″ = 1.94106423399 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    