# 14 21 22 triangle

### Acute scalene triangle.

Sides: a = 14   b = 21   c = 22

Area: T = 141.9366385398
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 37.91114752928° = 37°54'41″ = 0.66216800681 rad
Angle ∠ B = β = 67.17106966747° = 67°10'15″ = 1.17223498178 rad
Angle ∠ C = γ = 74.91878280325° = 74°55'4″ = 1.30875627676 rad

Height: ha = 20.27766264855
Height: hb = 13.51877509903
Height: hc = 12.90333077635

Median: ma = 20.33546994077
Median: mb = 15.15875063912
Median: mc = 14.05334693226

Inradius: r = 4.98802240491
Circumradius: R = 11.3922427639

Vertex coordinates: A[22; 0] B[0; 0] C[5.43218181818; 12.90333077635]
Centroid: CG[9.14439393939; 4.30111025878]
Coordinates of the circumscribed circle: U[11; 2.96443561714]
Coordinates of the inscribed circle: I[7.5; 4.98802240491]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.0898524707° = 142°5'19″ = 0.66216800681 rad
∠ B' = β' = 112.8299303325° = 112°49'45″ = 1.17223498178 rad
∠ C' = γ' = 105.0822171967° = 105°4'56″ = 1.30875627676 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    