# 9 17 20 triangle

### Obtuse scalene triangle.

Sides: a = 9   b = 17   c = 20

Area: T = 76.13114652427
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 26.60546816894° = 26°36'17″ = 0.46443392919 rad
Angle ∠ B = β = 57.76990473645° = 57°46'9″ = 1.00882600823 rad
Angle ∠ C = γ = 95.62662709461° = 95°37'35″ = 1.66989932794 rad

Height: ha = 16.91881033873
Height: hb = 8.95766429697
Height: hc = 7.61331465243

Median: ma = 18.00769431054
Median: mb = 12.97111217711
Median: mc = 9.22195444573

Inradius: r = 3.31100637062
Circumradius: R = 10.04884076795

Vertex coordinates: A[20; 0] B[0; 0] C[4.8; 7.61331465243]
Centroid: CG[8.26766666667; 2.53877155081]
Coordinates of the circumscribed circle: U[10; -0.98551380078]
Coordinates of the inscribed circle: I[6; 3.31100637062]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.3955318311° = 153°23'43″ = 0.46443392919 rad
∠ B' = β' = 122.2310952636° = 122°13'51″ = 1.00882600823 rad
∠ C' = γ' = 84.37437290539° = 84°22'25″ = 1.66989932794 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    