# 15 22 22 triangle

### Acute isosceles triangle.

Sides: a = 15   b = 22   c = 22

Area: T = 155.11658841
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 39.86545409444° = 39°51'52″ = 0.69657674943 rad
Angle ∠ B = β = 70.06877295278° = 70°4'4″ = 1.22329125797 rad
Angle ∠ C = γ = 70.06877295278° = 70°4'4″ = 1.22329125797 rad

Height: ha = 20.68221178799
Height: hb = 14.10114440091
Height: hc = 14.10114440091

Median: ma = 20.68221178799
Median: mb = 15.28107067899
Median: mc = 15.28107067899

Inradius: r = 5.25881655627
Circumradius: R = 11.70109293441

Vertex coordinates: A[22; 0] B[0; 0] C[5.11436363636; 14.10114440091]
Centroid: CG[9.03878787879; 4.77004813364]
Coordinates of the circumscribed circle: U[11; 3.98989531855]
Coordinates of the inscribed circle: I[7.5; 5.25881655627]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.1355459056° = 140°8'8″ = 0.69657674943 rad
∠ B' = β' = 109.9322270472° = 109°55'56″ = 1.22329125797 rad
∠ C' = γ' = 109.9322270472° = 109°55'56″ = 1.22329125797 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    