# 5 27 27 triangle

### Acute isosceles triangle.

Sides: a = 5   b = 27   c = 27

Area: T = 67.21100252939
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 10.62655494105° = 10°37'32″ = 0.1855450822 rad
Angle ∠ B = β = 84.68772252947° = 84°41'14″ = 1.47880709158 rad
Angle ∠ C = γ = 84.68772252947° = 84°41'14″ = 1.47880709158 rad

Height: ha = 26.88440101175
Height: hb = 4.97985203921
Height: hc = 4.97985203921

Median: ma = 26.88440101175
Median: mb = 13.9555285737
Median: mc = 13.9555285737

Inradius: r = 2.27883059422
Circumradius: R = 13.55882451579

Vertex coordinates: A[27; 0] B[0; 0] C[0.4632962963; 4.97985203921]
Centroid: CG[9.15443209877; 1.66595067974]
Coordinates of the circumscribed circle: U[13.5; 1.25553930702]
Coordinates of the inscribed circle: I[2.5; 2.27883059422]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.3744450589° = 169°22'28″ = 0.1855450822 rad
∠ B' = β' = 95.31327747053° = 95°18'46″ = 1.47880709158 rad
∠ C' = γ' = 95.31327747053° = 95°18'46″ = 1.47880709158 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    