# 20 26 27 triangle

### Acute scalene triangle.

Sides: a = 20   b = 26   c = 27

Area: T = 245.1010872092
Perimeter: p = 73
Semiperimeter: s = 36.5

Angle ∠ A = α = 44.29902177194° = 44°17'25″ = 0.77330101256 rad
Angle ∠ B = β = 65.22004820834° = 65°12'2″ = 1.13879630862 rad
Angle ∠ C = γ = 70.50993001972° = 70°30'33″ = 1.23106194417 rad

Height: ha = 24.51100872091
Height: hb = 18.85439132378
Height: hc = 18.15656201549

Median: ma = 24.54658754173
Median: mb = 19.88771818014
Median: mc = 18.86113361139

Inradius: r = 6.71550923861
Circumradius: R = 14.32106344802

Vertex coordinates: A[27; 0] B[0; 0] C[8.38988888889; 18.15656201549]
Centroid: CG[11.79662962963; 6.0521873385]
Coordinates of the circumscribed circle: U[13.5; 4.77881347737]
Coordinates of the inscribed circle: I[10.5; 6.71550923861]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.7109782281° = 135°42'35″ = 0.77330101256 rad
∠ B' = β' = 114.8799517917° = 114°47'58″ = 1.13879630862 rad
∠ C' = γ' = 109.4910699803° = 109°29'27″ = 1.23106194417 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    