9 11 12 triangle

Acute scalene triangle.

Sides: a = 9   b = 11   c = 12

Area: T = 47.32986382648
Perimeter: p = 32
Semiperimeter: s = 16

Angle ∠ A = α = 45.81656148467° = 45°48'56″ = 0.87996333279 rad
Angle ∠ B = β = 61.21877953194° = 61°13'4″ = 1.06884520891 rad
Angle ∠ C = γ = 72.96765898339° = 72°58' = 1.27435072366 rad

Height: ha = 10.517747517
Height: hb = 8.60552069572
Height: hc = 7.88881063775

Median: ma = 10.59548100502
Median: mb = 9.06991785736
Median: mc = 8.06222577483

Vertex coordinates: A[12; 0] B[0; 0] C[4.33333333333; 7.88881063775]
Centroid: CG[5.44444444444; 2.62993687925]
Coordinates of the circumscribed circle: U[6; 1.8388210504]
Coordinates of the inscribed circle: I[5; 2.95880398915]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.1844385153° = 134°11'4″ = 0.87996333279 rad
∠ B' = β' = 118.7822204681° = 118°46'56″ = 1.06884520891 rad
∠ C' = γ' = 107.0333410166° = 107°2' = 1.27435072366 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    