# 6 13 13 triangle

### Acute isosceles triangle.

Sides: a = 6   b = 13   c = 13

Area: T = 37.9477331922
Perimeter: p = 32
Semiperimeter: s = 16

Angle ∠ A = α = 26.68547275942° = 26°41'5″ = 0.46657363565 rad
Angle ∠ B = β = 76.65876362029° = 76°39'28″ = 1.33879281485 rad
Angle ∠ C = γ = 76.65876362029° = 76°39'28″ = 1.33879281485 rad

Height: ha = 12.64991106407
Height: hb = 5.83880510649
Height: hc = 5.83880510649

Median: ma = 12.64991106407
Median: mb = 7.76220873481
Median: mc = 7.76220873481

Inradius: r = 2.37217082451
Circumradius: R = 6.68803115571

Vertex coordinates: A[13; 0] B[0; 0] C[1.38546153846; 5.83880510649]
Centroid: CG[4.79548717949; 1.94660170216]
Coordinates of the circumscribed circle: U[6.5; 1.54216103593]
Coordinates of the inscribed circle: I[3; 2.37217082451]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.3155272406° = 153°18'55″ = 0.46657363565 rad
∠ B' = β' = 103.3422363797° = 103°20'32″ = 1.33879281485 rad
∠ C' = γ' = 103.3422363797° = 103°20'32″ = 1.33879281485 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    