# 5 9 12 triangle

### Obtuse scalene triangle.

Sides: a = 5   b = 9   c = 12

Area: T = 20.39660780544
Perimeter: p = 26
Semiperimeter: s = 13

Angle ∠ A = α = 22.19216065663° = 22°11'30″ = 0.38773166009 rad
Angle ∠ B = β = 42.83334280661° = 42°50' = 0.74875843497 rad
Angle ∠ C = γ = 114.9754965368° = 114°58'30″ = 2.0076691703 rad

Height: ha = 8.15884312217
Height: hb = 4.53224617899
Height: hc = 3.39993463424

Median: ma = 10.3087764064
Median: mb = 8.01656097709
Median: mc = 4.12331056256

Inradius: r = 1.56989290811
Circumradius: R = 6.61989195609

Vertex coordinates: A[12; 0] B[0; 0] C[3.66766666667; 3.39993463424]
Centroid: CG[5.22222222222; 1.13331154475]
Coordinates of the circumscribed circle: U[6; -2.79546549257]
Coordinates of the inscribed circle: I[4; 1.56989290811]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.8088393434° = 157°48'30″ = 0.38773166009 rad
∠ B' = β' = 137.1676571934° = 137°10' = 0.74875843497 rad
∠ C' = γ' = 65.02550346323° = 65°1'30″ = 2.0076691703 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    