# 7 13 13 triangle

### Acute isosceles triangle.

Sides: a = 7   b = 13   c = 13

Area: T = 43.82199440894
Perimeter: p = 33
Semiperimeter: s = 16.5

Angle ∠ A = α = 31.23769965513° = 31°14'13″ = 0.54551884383 rad
Angle ∠ B = β = 74.38215017244° = 74°22'53″ = 1.29882021077 rad
Angle ∠ C = γ = 74.38215017244° = 74°22'53″ = 1.29882021077 rad

Height: ha = 12.52199840255
Height: hb = 6.74215298599
Height: hc = 6.74215298599

Median: ma = 12.52199840255
Median: mb = 8.17700673192
Median: mc = 8.17700673192

Inradius: r = 2.65657541872
Circumradius: R = 6.74992098894

Vertex coordinates: A[13; 0] B[0; 0] C[1.88546153846; 6.74215298599]
Centroid: CG[4.96215384615; 2.247717662]
Coordinates of the circumscribed circle: U[6.5; 1.81770949702]
Coordinates of the inscribed circle: I[3.5; 2.65657541872]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.7633003449° = 148°45'47″ = 0.54551884383 rad
∠ B' = β' = 105.6188498276° = 105°37'7″ = 1.29882021077 rad
∠ C' = γ' = 105.6188498276° = 105°37'7″ = 1.29882021077 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    