# 12 23 23 triangle

### Acute isosceles triangle.

Sides: a = 12   b = 23   c = 23

Area: T = 133.2221619867
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 30.24333306298° = 30°14'36″ = 0.52878456963 rad
Angle ∠ B = β = 74.87883346851° = 74°52'42″ = 1.30768734787 rad
Angle ∠ C = γ = 74.87883346851° = 74°52'42″ = 1.30768734787 rad

Height: ha = 22.20436033112
Height: hb = 11.58444886841
Height: hc = 11.58444886841

Median: ma = 22.20436033112
Median: mb = 14.2921605928
Median: mc = 14.2921605928

Inradius: r = 4.59438489609
Circumradius: R = 11.9122480884

Vertex coordinates: A[23; 0] B[0; 0] C[3.13304347826; 11.58444886841]
Centroid: CG[8.71101449275; 3.8611496228]
Coordinates of the circumscribed circle: U[11.5; 3.10876037089]
Coordinates of the inscribed circle: I[6; 4.59438489609]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.757666937° = 149°45'24″ = 0.52878456963 rad
∠ B' = β' = 105.1221665315° = 105°7'18″ = 1.30768734787 rad
∠ C' = γ' = 105.1221665315° = 105°7'18″ = 1.30768734787 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.