# 13 21 23 triangle

### Acute scalene triangle.

Sides: a = 13   b = 21   c = 23

Area: T = 134.9989582931
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 33.9844117855° = 33°59'3″ = 0.593313475 rad
Angle ∠ B = β = 64.54772963821° = 64°32'50″ = 1.12765628451 rad
Angle ∠ C = γ = 81.46985857629° = 81°28'7″ = 1.42218950585 rad

Height: ha = 20.76876281433
Height: hb = 12.85661507554
Height: hc = 11.73882246027

Median: ma = 21.04216254125
Median: mb = 15.45215371404
Median: mc = 13.14334394281

Inradius: r = 4.73664765941
Circumradius: R = 11.62986750867

Vertex coordinates: A[23; 0] B[0; 0] C[5.58769565217; 11.73882246027]
Centroid: CG[9.52989855072; 3.91327415342]
Coordinates of the circumscribed circle: U[11.5; 1.72551331173]
Coordinates of the inscribed circle: I[7.5; 4.73664765941]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.0165882145° = 146°57″ = 0.593313475 rad
∠ B' = β' = 115.4532703618° = 115°27'10″ = 1.12765628451 rad
∠ C' = γ' = 98.53114142371° = 98°31'53″ = 1.42218950585 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 ### 6. Inradius ### 7. Circumradius ### 8. Calculation of medians #### Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.