# 21 21 23 triangle

### Acute isosceles triangle.

Sides: a = 21   b = 21   c = 23

Area: T = 202.0769758994
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 56.796617747° = 56°47'46″ = 0.99112802994 rad
Angle ∠ B = β = 56.796617747° = 56°47'46″ = 0.99112802994 rad
Angle ∠ C = γ = 66.40876450599° = 66°24'28″ = 1.15990320548 rad

Height: ha = 19.24547389518
Height: hb = 19.24547389518
Height: hc = 17.57112833908

Median: ma = 19.35884606826
Median: mb = 19.35884606826
Median: mc = 17.57112833908

Inradius: r = 6.2187531046
Circumradius: R = 12.54988841706

Vertex coordinates: A[23; 0] B[0; 0] C[11.5; 17.57112833908]
Centroid: CG[11.5; 5.85770944636]
Coordinates of the circumscribed circle: U[11.5; 5.02223992202]
Coordinates of the inscribed circle: I[11.5; 6.2187531046]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 123.204382253° = 123°12'14″ = 0.99112802994 rad
∠ B' = β' = 123.204382253° = 123°12'14″ = 0.99112802994 rad
∠ C' = γ' = 113.592235494° = 113°35'32″ = 1.15990320548 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.