# 5 13 13 triangle

### Acute isosceles triangle.

Sides: a = 5   b = 13   c = 13

Area: T = 31.89333770554
Perimeter: p = 31
Semiperimeter: s = 15.5

Angle ∠ A = α = 22.17549784219° = 22°10'30″ = 0.3877026385 rad
Angle ∠ B = β = 78.9132510789° = 78°54'45″ = 1.37772831343 rad
Angle ∠ C = γ = 78.9132510789° = 78°54'45″ = 1.37772831343 rad

Height: ha = 12.75773508222
Height: hb = 4.90766733931
Height: hc = 4.90766733931

Median: ma = 12.75773508222
Median: mb = 7.39993242935
Median: mc = 7.39993242935

Inradius: r = 2.05876372294
Circumradius: R = 6.62436322241

Vertex coordinates: A[13; 0] B[0; 0] C[0.96215384615; 4.90766733931]
Centroid: CG[4.65438461538; 1.63655577977]
Coordinates of the circumscribed circle: U[6.5; 1.27437754277]
Coordinates of the inscribed circle: I[2.5; 2.05876372294]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.8255021578° = 157°49'30″ = 0.3877026385 rad
∠ B' = β' = 101.0877489211° = 101°5'15″ = 1.37772831343 rad
∠ C' = γ' = 101.0877489211° = 101°5'15″ = 1.37772831343 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    