# 3 23 23 triangle

### Acute isosceles triangle.

Sides: a = 3   b = 23   c = 23

Area: T = 34.42765522526
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 7.47986704631° = 7°28'43″ = 0.13105274233 rad
Angle ∠ B = β = 86.26106647685° = 86°15'38″ = 1.50655326152 rad
Angle ∠ C = γ = 86.26106647685° = 86°15'38″ = 1.50655326152 rad

Height: ha = 22.95110348351
Height: hb = 2.99436132394
Height: hc = 2.99436132394

Median: ma = 22.95110348351
Median: mb = 11.69440155635
Median: mc = 11.69440155635

Inradius: r = 1.40551653981
Circumradius: R = 11.52545348151

Vertex coordinates: A[23; 0] B[0; 0] C[0.19656521739; 2.99436132394]
Centroid: CG[7.7321884058; 0.99878710798]
Coordinates of the circumscribed circle: U[11.5; 0.75216000966]
Coordinates of the inscribed circle: I[1.5; 1.40551653981]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 172.5211329537° = 172°31'17″ = 0.13105274233 rad
∠ B' = β' = 93.73993352315° = 93°44'22″ = 1.50655326152 rad
∠ C' = γ' = 93.73993352315° = 93°44'22″ = 1.50655326152 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    