# 11.5 13.7 12.2 triangle

### Acute scalene triangle.

Sides: a = 11.5   b = 13.7   c = 12.2

Area: T = 66.15498299318
Perimeter: p = 37.4
Semiperimeter: s = 18.7

Angle ∠ A = α = 52.33105942326° = 52°19'50″ = 0.91333411689 rad
Angle ∠ B = β = 70.55876536542° = 70°33'28″ = 1.23114633687 rad
Angle ∠ C = γ = 57.11217521133° = 57°6'42″ = 0.9976788116 rad

Height: ha = 11.5044318249
Height: hb = 9.65769094791
Height: hc = 10.8444234415

Median: ma = 11.62876609858
Median: mb = 9.67658720537
Median: mc = 11.08797111876

Vertex coordinates: A[12.2; 0] B[0; 0] C[3.82878688525; 10.8444234415]
Centroid: CG[5.34326229508; 3.6154744805]
Coordinates of the circumscribed circle: U[6.1; 3.94444923784]
Coordinates of the inscribed circle: I[5; 3.53774240605]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.6699405767° = 127°40'10″ = 0.91333411689 rad
∠ B' = β' = 109.4422346346° = 109°26'32″ = 1.23114633687 rad
∠ C' = γ' = 122.8888247887° = 122°53'18″ = 0.9976788116 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    