# 15 19 20 triangle

### Acute scalene triangle.

Sides: a = 15   b = 19   c = 20

Area: T = 134.7699665924
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 45.14991919008° = 45°8'57″ = 0.78880020533 rad
Angle ∠ B = β = 63.89661188627° = 63°53'46″ = 1.11551976534 rad
Angle ∠ C = γ = 70.95546892365° = 70°57'17″ = 1.23883929469 rad

Height: ha = 17.96599554565
Height: hb = 14.17989122025
Height: hc = 13.47699665924

Median: ma = 18.00769431054
Median: mb = 14.90880515159
Median: mc = 13.89224439894

Inradius: r = 4.98988765157
Circumradius: R = 10.57990908257

Vertex coordinates: A[20; 0] B[0; 0] C[6.6; 13.47699665924]
Centroid: CG[8.86766666667; 4.49899888641]
Coordinates of the circumscribed circle: U[10; 3.45221243747]
Coordinates of the inscribed circle: I[8; 4.98988765157]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.8510808099° = 134°51'3″ = 0.78880020533 rad
∠ B' = β' = 116.1043881137° = 116°6'14″ = 1.11551976534 rad
∠ C' = γ' = 109.0455310763° = 109°2'43″ = 1.23883929469 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    