# 21 27 27 triangle

### Acute isosceles triangle.

Sides: a = 21   b = 27   c = 27

Area: T = 261.184420224
Perimeter: p = 75
Semiperimeter: s = 37.5

Angle ∠ A = α = 45.77107609523° = 45°46'15″ = 0.79988504798 rad
Angle ∠ B = β = 67.11546195238° = 67°6'53″ = 1.17113710869 rad
Angle ∠ C = γ = 67.11546195238° = 67°6'53″ = 1.17113710869 rad

Height: ha = 24.87546859277
Height: hb = 19.34769779437
Height: hc = 19.34769779437

Median: ma = 24.87546859277
Median: mb = 20.06986322404
Median: mc = 20.06986322404

Inradius: r = 6.96549120597
Circumradius: R = 14.65334513465

Vertex coordinates: A[27; 0] B[0; 0] C[8.16766666667; 19.34769779437]
Centroid: CG[11.72222222222; 6.44989926479]
Coordinates of the circumscribed circle: U[13.5; 5.69985644125]
Coordinates of the inscribed circle: I[10.5; 6.96549120597]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.2299239048° = 134°13'45″ = 0.79988504798 rad
∠ B' = β' = 112.8855380476° = 112°53'7″ = 1.17113710869 rad
∠ C' = γ' = 112.8855380476° = 112°53'7″ = 1.17113710869 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    