# 9 27 27 triangle

### Acute isosceles triangle.

Sides: a = 9   b = 27   c = 27

Area: T = 119.8010615608
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 19.18881364537° = 19°11'17″ = 0.33548961584 rad
Angle ∠ B = β = 80.40659317731° = 80°24'21″ = 1.40333482476 rad
Angle ∠ C = γ = 80.40659317731° = 80°24'21″ = 1.40333482476 rad

Height: ha = 26.62223590239
Height: hb = 8.87441196746
Height: hc = 8.87441196746

Median: ma = 26.62223590239
Median: mb = 14.92548115566
Median: mc = 14.92548115566

Inradius: r = 3.80331941463
Circumradius: R = 13.69114989266

Vertex coordinates: A[27; 0] B[0; 0] C[1.5; 8.87441196746]
Centroid: CG[9.5; 2.95880398915]
Coordinates of the circumscribed circle: U[13.5; 2.28219164878]
Coordinates of the inscribed circle: I[4.5; 3.80331941463]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.8121863546° = 160°48'43″ = 0.33548961584 rad
∠ B' = β' = 99.59440682269° = 99°35'39″ = 1.40333482476 rad
∠ C' = γ' = 99.59440682269° = 99°35'39″ = 1.40333482476 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    