# 15 16 20 triangle

### Acute scalene triangle.

Sides: a = 15   b = 16   c = 20

Area: T = 118.2799066195
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 47.66770696613° = 47°40'1″ = 0.83219473104 rad
Angle ∠ B = β = 52.04880797108° = 52°2'53″ = 0.90884103603 rad
Angle ∠ C = γ = 80.28548506279° = 80°17'5″ = 1.40112349829 rad

Height: ha = 15.77105421594
Height: hb = 14.78548832744
Height: hc = 11.82879066195

Median: ma = 16.48548415218
Median: mb = 15.76438827704
Median: mc = 11.85332695911

Inradius: r = 4.63883947528
Circumradius: R = 10.14554977504

Vertex coordinates: A[20; 0] B[0; 0] C[9.225; 11.82879066195]
Centroid: CG[9.74216666667; 3.94326355398]
Coordinates of the circumscribed circle: U[10; 1.71220527454]
Coordinates of the inscribed circle: I[9.5; 4.63883947528]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.3332930339° = 132°19'59″ = 0.83219473104 rad
∠ B' = β' = 127.9521920289° = 127°57'7″ = 0.90884103603 rad
∠ C' = γ' = 99.71551493721° = 99°42'55″ = 1.40112349829 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    