# 13 23 26 triangle

### Acute scalene triangle.

Sides: a = 13   b = 23   c = 26

Area: T = 149.3998795176
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 29.97876090229° = 29°58'39″ = 0.52332079793 rad
Angle ∠ B = β = 62.1310738238° = 62°7'51″ = 1.08443859489 rad
Angle ∠ C = γ = 87.89216527391° = 87°53'30″ = 1.53439987253 rad

Height: ha = 22.98444300271
Height: hb = 12.99111995805
Height: hc = 11.49222150135

Median: ma = 23.67696007571
Median: mb = 17.03767250374
Median: mc = 13.4166407865

Inradius: r = 4.81993159734
Circumradius: R = 13.0098806381

Vertex coordinates: A[26; 0] B[0; 0] C[6.07769230769; 11.49222150135]
Centroid: CG[10.69223076923; 3.83107383378]
Coordinates of the circumscribed circle: U[13; 0.47985848501]
Coordinates of the inscribed circle: I[8; 4.81993159734]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.0222390977° = 150°1'21″ = 0.52332079793 rad
∠ B' = β' = 117.8699261762° = 117°52'9″ = 1.08443859489 rad
∠ C' = γ' = 92.10883472609° = 92°6'30″ = 1.53439987253 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    