# 20 21 23 triangle

### Acute scalene triangle.

Sides: a = 20   b = 21   c = 23

Area: T = 194.9776921711
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 53.83985840336° = 53°50'19″ = 0.9439660556 rad
Angle ∠ B = β = 57.96551639558° = 57°57'55″ = 1.01216829625 rad
Angle ∠ C = γ = 68.19662520106° = 68°11'47″ = 1.19902491351 rad

Height: ha = 19.49876921711
Height: hb = 18.56992306392
Height: hc = 16.95545149314

Median: ma = 19.62114168703
Median: mb = 18.82215302247
Median: mc = 16.97879268463

Inradius: r = 6.09330288035
Circumradius: R = 12.38660812798

Vertex coordinates: A[23; 0] B[0; 0] C[10.60986956522; 16.95545149314]
Centroid: CG[11.20328985507; 5.65215049771]
Coordinates of the circumscribed circle: U[11.5; 4.60105444754]
Coordinates of the inscribed circle: I[11; 6.09330288035]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.1611415966° = 126°9'41″ = 0.9439660556 rad
∠ B' = β' = 122.0354836044° = 122°2'5″ = 1.01216829625 rad
∠ C' = γ' = 111.8043747989° = 111°48'13″ = 1.19902491351 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    