# 12 21 23 triangle

### Acute scalene triangle.

Sides: a = 12   b = 21   c = 23

Area: T = 125.221980674
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 31.232225881° = 31°13'56″ = 0.54551057491 rad
Angle ∠ B = β = 65.14771113984° = 65°8'50″ = 1.13770315921 rad
Angle ∠ C = γ = 83.62106297916° = 83°37'14″ = 1.45994553125 rad

Height: ha = 20.876996779
Height: hb = 11.926569588
Height: hc = 10.8898678847

Median: ma = 21.19896201004
Median: mb = 15.04216089565
Median: mc = 12.65989889012

Inradius: r = 4.4722135955
Circumradius: R = 11.57216517836

Vertex coordinates: A[23; 0] B[0; 0] C[5.04334782609; 10.8898678847]
Centroid: CG[9.3487826087; 3.63295596157]
Coordinates of the circumscribed circle: U[11.5; 1.28657390871]
Coordinates of the inscribed circle: I[7; 4.4722135955]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.768774119° = 148°46'4″ = 0.54551057491 rad
∠ B' = β' = 114.8532888602° = 114°51'10″ = 1.13770315921 rad
∠ C' = γ' = 96.37993702084° = 96°22'46″ = 1.45994553125 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.