# 13 13 23 triangle

### Obtuse isosceles triangle.

Sides: a = 13   b = 13   c = 23

Area: T = 69.71550450046
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 27.7965772496° = 27°47'45″ = 0.48551277482 rad
Angle ∠ B = β = 27.7965772496° = 27°47'45″ = 0.48551277482 rad
Angle ∠ C = γ = 124.4088455008° = 124°24'30″ = 2.17113371572 rad

Height: ha = 10.72553915392
Height: hb = 10.72553915392
Height: hc = 6.06221778265

Median: ma = 17.51442798881
Median: mb = 17.51442798881
Median: mc = 6.06221778265

Inradius: r = 2.8465512041
Circumradius: R = 13.93988850704

Vertex coordinates: A[23; 0] B[0; 0] C[11.5; 6.06221778265]
Centroid: CG[11.5; 2.02107259422]
Coordinates of the circumscribed circle: U[11.5; -7.87767072439]
Coordinates of the inscribed circle: I[11.5; 2.8465512041]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.2044227504° = 152°12'15″ = 0.48551277482 rad
∠ B' = β' = 152.2044227504° = 152°12'15″ = 0.48551277482 rad
∠ C' = γ' = 55.59215449921° = 55°35'30″ = 2.17113371572 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    