# 11 19 20 triangle

### Acute scalene triangle.

Sides: a = 11   b = 19   c = 20

Area: T = 102.476950766
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 32.63768975036° = 32°38'13″ = 0.57696213191 rad
Angle ∠ B = β = 68.67663137365° = 68°40'35″ = 1.19986277928 rad
Angle ∠ C = γ = 78.68767887599° = 78°41'12″ = 1.37333435417 rad

Height: ha = 18.63108195745
Height: hb = 10.78662639642
Height: hc = 10.2476950766

Median: ma = 18.71549672722
Median: mb = 13.04879883507
Median: mc = 11.8744342087

Inradius: r = 4.09987803064
Circumradius: R = 10.19881557623

Vertex coordinates: A[20; 0] B[0; 0] C[4; 10.2476950766]
Centroid: CG[8; 3.41656502553]
Coordinates of the circumscribed circle: U[10; 2.00105951495]
Coordinates of the inscribed circle: I[6; 4.09987803064]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.3633102496° = 147°21'47″ = 0.57696213191 rad
∠ B' = β' = 111.3243686263° = 111°19'25″ = 1.19986277928 rad
∠ C' = γ' = 101.313321124° = 101°18'48″ = 1.37333435417 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    