# 6 23 27 triangle

### Obtuse scalene triangle.

Sides: a = 6   b = 23   c = 27

Area: T = 55.4987747702
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 10.29661852424° = 10°17'46″ = 0.18797023329 rad
Angle ∠ B = β = 43.24879853748° = 43°14'53″ = 0.75548197396 rad
Angle ∠ C = γ = 126.4565829383° = 126°27'21″ = 2.20770705811 rad

Height: ha = 18.4999249234
Height: hb = 4.82658911045
Height: hc = 4.11109442742

Median: ma = 24.9899799196
Median: mb = 15.81992920196
Median: mc = 10.01224921973

Inradius: r = 1.98220624179
Circumradius: R = 16.784446493

Vertex coordinates: A[27; 0] B[0; 0] C[4.37703703704; 4.11109442742]
Centroid: CG[10.45767901235; 1.37703147581]
Coordinates of the circumscribed circle: U[13.5; -9.9733377712]
Coordinates of the inscribed circle: I[5; 1.98220624179]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.7043814758° = 169°42'14″ = 0.18797023329 rad
∠ B' = β' = 136.7522014625° = 136°45'7″ = 0.75548197396 rad
∠ C' = γ' = 53.54441706172° = 53°32'39″ = 2.20770705811 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    