# 18 23 23 triangle

### Acute isosceles triangle.

Sides: a = 18   b = 23   c = 23

Area: T = 190.4944094397
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 46.07113682119° = 46°4'17″ = 0.80440970662 rad
Angle ∠ B = β = 66.96443158941° = 66°57'52″ = 1.16987477937 rad
Angle ∠ C = γ = 66.96443158941° = 66°57'52″ = 1.16987477937 rad

Height: ha = 21.16660104885
Height: hb = 16.56547038606
Height: hc = 16.56547038606

Median: ma = 21.16660104885
Median: mb = 17.15437167984
Median: mc = 17.15437167984

Inradius: r = 5.95329404499
Circumradius: R = 12.49664503889

Vertex coordinates: A[23; 0] B[0; 0] C[7.04334782609; 16.56547038606]
Centroid: CG[10.01444927536; 5.52215679535]
Coordinates of the circumscribed circle: U[11.5; 4.89899153696]
Coordinates of the inscribed circle: I[9; 5.95329404499]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.9298631788° = 133°55'43″ = 0.80440970662 rad
∠ B' = β' = 113.0365684106° = 113°2'8″ = 1.16987477937 rad
∠ C' = γ' = 113.0365684106° = 113°2'8″ = 1.16987477937 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    