# 17 22 22 triangle

### Acute isosceles triangle.

Sides: a = 17   b = 22   c = 22

Area: T = 172.4798803046
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 45.4576845195° = 45°27'25″ = 0.79333716162 rad
Angle ∠ B = β = 67.27215774025° = 67°16'18″ = 1.17441105187 rad
Angle ∠ C = γ = 67.27215774025° = 67°16'18″ = 1.17441105187 rad

Height: ha = 20.29216238877
Height: hb = 15.6879891186
Height: hc = 15.6879891186

Median: ma = 20.29216238877
Median: mb = 16.29441707368
Median: mc = 16.29441707368

Inradius: r = 5.65550427228
Circumradius: R = 11.92661031714

Vertex coordinates: A[22; 0] B[0; 0] C[6.56881818182; 15.6879891186]
Centroid: CG[9.52327272727; 5.22766303953]
Coordinates of the circumscribed circle: U[11; 4.6087812589]
Coordinates of the inscribed circle: I[8.5; 5.65550427228]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.5433154805° = 134°32'35″ = 0.79333716162 rad
∠ B' = β' = 112.7288422598° = 112°43'42″ = 1.17441105187 rad
∠ C' = γ' = 112.7288422598° = 112°43'42″ = 1.17441105187 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    