# 3 27 27 triangle

### Acute isosceles triangle.

Sides: a = 3   b = 27   c = 27

Area: T = 40.43774517001
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 6.36994770734° = 6°22'10″ = 0.11111683466 rad
Angle ∠ B = β = 86.81552614633° = 86°48'55″ = 1.51552121535 rad
Angle ∠ C = γ = 86.81552614633° = 86°48'55″ = 1.51552121535 rad

Height: ha = 26.95883011334
Height: hb = 2.99553667926
Height: hc = 2.99553667926

Median: ma = 26.95883011334
Median: mb = 13.66656503687
Median: mc = 13.66656503687

Inradius: r = 1.41988579544
Circumradius: R = 13.5210881683

Vertex coordinates: A[27; 0] B[0; 0] C[0.16766666667; 2.99553667926]
Centroid: CG[9.05655555556; 0.99884555975]
Coordinates of the circumscribed circle: U[13.5; 0.75111600935]
Coordinates of the inscribed circle: I[1.5; 1.41988579544]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.6310522927° = 173°37'50″ = 0.11111683466 rad
∠ B' = β' = 93.18547385367° = 93°11'5″ = 1.51552121535 rad
∠ C' = γ' = 93.18547385367° = 93°11'5″ = 1.51552121535 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    