# 20 23 27 triangle

### Acute scalene triangle.

Sides: a = 20   b = 23   c = 27

Area: T = 224.4999443206
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 46.30548463945° = 46°18'17″ = 0.80881720292 rad
Angle ∠ B = β = 56.25110114041° = 56°15'4″ = 0.98217653566 rad
Angle ∠ C = γ = 77.44441422014° = 77°26'39″ = 1.35216552678 rad

Height: ha = 22.45499443206
Height: hb = 19.52216907136
Height: hc = 16.63295883857

Median: ma = 23
Median: mb = 20.79106228863
Median: mc = 16.88002976164

Inradius: r = 6.41442698059
Circumradius: R = 13.8310769269

Vertex coordinates: A[27; 0] B[0; 0] C[11.11111111111; 16.63295883857]
Centroid: CG[12.70437037037; 5.54331961286]
Coordinates of the circumscribed circle: U[13.5; 3.00766889715]
Coordinates of the inscribed circle: I[12; 6.41442698059]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.6955153606° = 133°41'43″ = 0.80881720292 rad
∠ B' = β' = 123.7498988596° = 123°44'56″ = 0.98217653566 rad
∠ C' = γ' = 102.5565857799° = 102°33'21″ = 1.35216552678 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    