# 20 21 28 triangle

### Acute scalene triangle.

Sides: a = 20   b = 21   c = 28

Area: T = 209.5165960013
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 45.4550065407° = 45°27' = 0.79332532866 rad
Angle ∠ B = β = 48.44108524081° = 48°26'27″ = 0.8455452367 rad
Angle ∠ C = γ = 86.10990821848° = 86°6'33″ = 1.5032887 rad

Height: ha = 20.95215960013
Height: hb = 19.95439009536
Height: hc = 14.96554257152

Median: ma = 22.63884628453
Median: mb = 21.94988040676
Median: mc = 14.98333240638

Inradius: r = 6.07329263772
Circumradius: R = 14.03223438836

Vertex coordinates: A[28; 0] B[0; 0] C[13.26878571429; 14.96554257152]
Centroid: CG[13.7565952381; 4.98884752384]
Coordinates of the circumscribed circle: U[14; 0.95221947635]
Coordinates of the inscribed circle: I[13.5; 6.07329263772]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.5549934593° = 134°33' = 0.79332532866 rad
∠ B' = β' = 131.5599147592° = 131°33'33″ = 0.8455452367 rad
∠ C' = γ' = 93.89109178152° = 93°53'27″ = 1.5032887 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    