# 8 21 22 triangle

### Acute scalene triangle.

Sides: a = 8   b = 21   c = 22

Area: T = 83.8365776969
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 21.28799664684° = 21°16'48″ = 0.37114054796 rad
Angle ∠ B = β = 72.30333552301° = 72°18'12″ = 1.2621931609 rad
Angle ∠ C = γ = 86.41766783015° = 86°25' = 1.5088255565 rad

Height: ha = 20.95989442423
Height: hb = 7.98443597113
Height: hc = 7.62114342699

Median: ma = 21.13105466091
Median: mb = 12.79664838921
Median: mc = 11.46773449412

Inradius: r = 3.28876775282
Circumradius: R = 11.02215475231

Vertex coordinates: A[22; 0] B[0; 0] C[2.43218181818; 7.62114342699]
Centroid: CG[8.14439393939; 2.544047809]
Coordinates of the circumscribed circle: U[11; 0.68988467202]
Coordinates of the inscribed circle: I[4.5; 3.28876775282]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.7220033532° = 158°43'12″ = 0.37114054796 rad
∠ B' = β' = 107.697664477° = 107°41'48″ = 1.2621931609 rad
∠ C' = γ' = 93.58333216985° = 93°35' = 1.5088255565 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    