# 19 20 27 triangle

### Acute scalene triangle.

Sides: a = 19   b = 20   c = 27

Area: T = 189.8321504235
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 44.67546095644° = 44°40'29″ = 0.78797190289 rad
Angle ∠ B = β = 47.73985577002° = 47°44'19″ = 0.8333195012 rad
Angle ∠ C = γ = 87.58768327354° = 87°35'13″ = 1.52986786126 rad

Height: ha = 19.98222636037
Height: hb = 18.98331504235
Height: hc = 14.06215929063

Median: ma = 21.77772817404
Median: mb = 21.09550231097
Median: mc = 14.08801278403

Inradius: r = 5.75224698253
Circumradius: R = 13.5121982694

Vertex coordinates: A[27; 0] B[0; 0] C[12.77877777778; 14.06215929063]
Centroid: CG[13.25992592593; 4.68771976354]
Coordinates of the circumscribed circle: U[13.5; 0.56989255871]
Coordinates of the inscribed circle: I[13; 5.75224698253]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.3255390436° = 135°19'31″ = 0.78797190289 rad
∠ B' = β' = 132.26114423° = 132°15'41″ = 0.8333195012 rad
∠ C' = γ' = 92.41331672646° = 92°24'47″ = 1.52986786126 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    