# 18 22 27 triangle

### Acute scalene triangle.

Sides: a = 18   b = 22   c = 27

Area: T = 197.0132531327
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 41.55552425328° = 41°33'19″ = 0.72552758037 rad
Angle ∠ B = β = 54.16993866083° = 54°10'10″ = 0.94554341501 rad
Angle ∠ C = γ = 84.27553708589° = 84°16'31″ = 1.47108826998 rad

Height: ha = 21.89902812586
Height: hb = 17.91102301207
Height: hc = 14.59435208391

Median: ma = 22.92437867727
Median: mb = 20.13770305656
Median: mc = 14.89112726118

Inradius: r = 5.88109710844
Circumradius: R = 13.56876648688

Vertex coordinates: A[27; 0] B[0; 0] C[10.5377037037; 14.59435208391]
Centroid: CG[12.5122345679; 4.86545069464]
Coordinates of the circumscribed circle: U[13.5; 1.35333403089]
Coordinates of the inscribed circle: I[11.5; 5.88109710844]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.4454757467° = 138°26'41″ = 0.72552758037 rad
∠ B' = β' = 125.8310613392° = 125°49'50″ = 0.94554341501 rad
∠ C' = γ' = 95.72546291411° = 95°43'29″ = 1.47108826998 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    