# 12 22 22 triangle

### Acute isosceles triangle.

Sides: a = 12   b = 22   c = 22

Area: T = 126.9966062931
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 31.65332402637° = 31°39'12″ = 0.55224532615 rad
Angle ∠ B = β = 74.17333798681° = 74°10'24″ = 1.2954569696 rad
Angle ∠ C = γ = 74.17333798681° = 74°10'24″ = 1.2954569696 rad

Height: ha = 21.16660104885
Height: hb = 11.54550966301
Height: hc = 11.54550966301

Median: ma = 21.16660104885
Median: mb = 13.89224439894
Median: mc = 13.89224439894

Inradius: r = 4.53655736761
Circumradius: R = 11.43334253085

Vertex coordinates: A[22; 0] B[0; 0] C[3.27327272727; 11.54550966301]
Centroid: CG[8.42442424242; 3.84883655434]
Coordinates of the circumscribed circle: U[11; 3.11882069023]
Coordinates of the inscribed circle: I[6; 4.53655736761]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.3476759736° = 148°20'48″ = 0.55224532615 rad
∠ B' = β' = 105.8276620132° = 105°49'36″ = 1.2954569696 rad
∠ C' = γ' = 105.8276620132° = 105°49'36″ = 1.2954569696 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    