# 20 22 27 triangle

### Acute scalene triangle.

Sides: a = 20   b = 22   c = 27

Area: T = 216.566047077
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 46.81660061647° = 46°48'58″ = 0.81770934502 rad
Angle ∠ B = β = 53.32987880616° = 53°19'44″ = 0.93107629378 rad
Angle ∠ C = γ = 79.85552057737° = 79°51'19″ = 1.39437362656 rad

Height: ha = 21.6566047077
Height: hb = 19.68773155245
Height: hc = 16.04215163533

Median: ma = 22.50655548699
Median: mb = 21.05994396887
Median: mc = 16.11767614613

Inradius: r = 6.27771150948
Circumradius: R = 13.71444142209

Vertex coordinates: A[27; 0] B[0; 0] C[11.94444444444; 16.04215163533]
Centroid: CG[12.98114814815; 5.34771721178]
Coordinates of the circumscribed circle: U[13.5; 2.41656070503]
Coordinates of the inscribed circle: I[12.5; 6.27771150948]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.1843993835° = 133°11'2″ = 0.81770934502 rad
∠ B' = β' = 126.6711211938° = 126°40'16″ = 0.93107629378 rad
∠ C' = γ' = 100.1454794226° = 100°8'41″ = 1.39437362656 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    