# 5 6 9 triangle

### Obtuse scalene triangle.

Sides: a = 5   b = 6   c = 9

Area: T = 14.14221356237
Perimeter: p = 20
Semiperimeter: s = 10

Angle ∠ A = α = 31.58663380965° = 31°35'11″ = 0.55112855984 rad
Angle ∠ B = β = 38.9422441269° = 38°56'33″ = 0.68796738189 rad
Angle ∠ C = γ = 109.4711220634° = 109°28'16″ = 1.91106332362 rad

Height: ha = 5.65768542495
Height: hb = 4.71440452079
Height: hc = 3.14326968053

Median: ma = 7.22884161474
Median: mb = 6.63332495807
Median: mc = 3.20215621187

Inradius: r = 1.41442135624
Circumradius: R = 4.7732970773

Vertex coordinates: A[9; 0] B[0; 0] C[3.88988888889; 3.14326968053]
Centroid: CG[4.29662962963; 1.04875656018]
Coordinates of the circumscribed circle: U[4.5; -1.59109902577]
Coordinates of the inscribed circle: I[4; 1.41442135624]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.4143661903° = 148°24'49″ = 0.55112855984 rad
∠ B' = β' = 141.0587558731° = 141°3'27″ = 0.68796738189 rad
∠ C' = γ' = 70.52987793655° = 70°31'44″ = 1.91106332362 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    