# 23 23 30 triangle

### Acute isosceles triangle.

Sides: a = 23   b = 23   c = 30

Area: T = 261.5343936612
Perimeter: p = 76
Semiperimeter: s = 38

Angle ∠ A = α = 49.2944293169° = 49°17'39″ = 0.86603477182 rad
Angle ∠ B = β = 49.2944293169° = 49°17'39″ = 0.86603477182 rad
Angle ∠ C = γ = 81.41114136621° = 81°24'41″ = 1.42108972171 rad

Height: ha = 22.74220814446
Height: hb = 22.74220814446
Height: hc = 17.43655957742

Median: ma = 24.1329857024
Median: mb = 24.1329857024
Median: mc = 17.43655957742

Inradius: r = 6.88224720161
Circumradius: R = 15.17701154022

Vertex coordinates: A[30; 0] B[0; 0] C[15; 17.43655957742]
Centroid: CG[15; 5.81218652581]
Coordinates of the circumscribed circle: U[15; 2.2655480372]
Coordinates of the inscribed circle: I[15; 6.88224720161]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.7065706831° = 130°42'21″ = 0.86603477182 rad
∠ B' = β' = 130.7065706831° = 130°42'21″ = 0.86603477182 rad
∠ C' = γ' = 98.58985863379° = 98°35'19″ = 1.42108972171 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    