# 21 23 23 triangle

### Acute isosceles triangle.

Sides: a = 21   b = 23   c = 23

Area: T = 214.8665510262
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 54.32657768443° = 54°19'33″ = 0.94881636746 rad
Angle ∠ B = β = 62.83771115778° = 62°50'14″ = 1.09767144895 rad
Angle ∠ C = γ = 62.83771115778° = 62°50'14″ = 1.09767144895 rad

Height: ha = 20.46333819297
Height: hb = 18.68439574141
Height: hc = 18.68439574141

Median: ma = 20.46333819297
Median: mb = 18.7821639971
Median: mc = 18.7821639971

Inradius: r = 6.41438958287
Circumradius: R = 12.92655272129

Vertex coordinates: A[23; 0] B[0; 0] C[9.58769565217; 18.68439574141]
Centroid: CG[10.86223188406; 6.22879858047]
Coordinates of the circumscribed circle: U[11.5; 5.90107841624]
Coordinates of the inscribed circle: I[10.5; 6.41438958287]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.6744223156° = 125°40'27″ = 0.94881636746 rad
∠ B' = β' = 117.1632888422° = 117°9'46″ = 1.09767144895 rad
∠ C' = γ' = 117.1632888422° = 117°9'46″ = 1.09767144895 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    