# 13 21 22 triangle

### Acute scalene triangle.

Sides: a = 13   b = 21   c = 22

Area: T = 132.8165661727
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 35.09768012276° = 35°5'48″ = 0.61325547383 rad
Angle ∠ B = β = 68.24655625695° = 68°14'44″ = 1.19111097667 rad
Angle ∠ C = γ = 76.65876362029° = 76°39'28″ = 1.33879281485 rad

Height: ha = 20.43331787272
Height: hb = 12.64991106407
Height: hc = 12.07441510661

Median: ma = 20.5
Median: mb = 14.70554411699
Median: mc = 13.56546599663

Inradius: r = 4.74334164903
Circumradius: R = 11.30551426351

Vertex coordinates: A[22; 0] B[0; 0] C[4.81881818182; 12.07441510661]
Centroid: CG[8.93993939394; 4.0254717022]
Coordinates of the circumscribed circle: U[11; 2.60988790696]
Coordinates of the inscribed circle: I[7; 4.74334164903]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.9033198772° = 144°54'12″ = 0.61325547383 rad
∠ B' = β' = 111.754443743° = 111°45'16″ = 1.19111097667 rad
∠ C' = γ' = 103.3422363797° = 103°20'32″ = 1.33879281485 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.