# 4 20 23 triangle

### Obtuse scalene triangle.

Sides: a = 4   b = 20   c = 23

Area: T = 28.31985010197
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 7.07224272592° = 7°4'21″ = 0.12334371418 rad
Angle ∠ B = β = 37.99769544166° = 37°59'49″ = 0.66331719603 rad
Angle ∠ C = γ = 134.9310618324° = 134°55'50″ = 2.35549835515 rad

Height: ha = 14.15992505098
Height: hb = 2.8321850102
Height: hc = 2.46224783495

Median: ma = 21.45992637339
Median: mb = 13.13439255366
Median: mc = 8.70334475928

Inradius: r = 1.20550425966
Circumradius: R = 16.24437976389

Vertex coordinates: A[23; 0] B[0; 0] C[3.1522173913; 2.46224783495]
Centroid: CG[8.71773913043; 0.82108261165]
Coordinates of the circumscribed circle: U[11.5; -11.47221820825]
Coordinates of the inscribed circle: I[3.5; 1.20550425966]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 172.9287572741° = 172°55'39″ = 0.12334371418 rad
∠ B' = β' = 142.0033045583° = 142°11″ = 0.66331719603 rad
∠ C' = γ' = 45.06993816758° = 45°4'10″ = 2.35549835515 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    