# 18 23 27 triangle

### Acute scalene triangle.

Sides: a = 18   b = 23   c = 27

Area: T = 204.6665580887
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 41.23549578936° = 41°14'6″ = 0.72196857822 rad
Angle ∠ B = β = 57.37879709914° = 57°22'41″ = 1.00114345119 rad
Angle ∠ C = γ = 81.3877071115° = 81°23'13″ = 1.42204723595 rad

Height: ha = 22.74106200986
Height: hb = 17.79770070337
Height: hc = 15.16604133991

Median: ma = 23.40993998214
Median: mb = 19.85657296517
Median: mc = 15.62884996081

Inradius: r = 6.02195759085
Circumradius: R = 13.65439812307

Vertex coordinates: A[27; 0] B[0; 0] C[9.70437037037; 15.16604133991]
Centroid: CG[12.23545679012; 5.0533471133]
Coordinates of the circumscribed circle: U[13.5; 2.04547991215]
Coordinates of the inscribed circle: I[11; 6.02195759085]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.7655042106° = 138°45'54″ = 0.72196857822 rad
∠ B' = β' = 122.6222029009° = 122°37'19″ = 1.00114345119 rad
∠ C' = γ' = 98.6132928885° = 98°36'47″ = 1.42204723595 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    