# 5 20 23 triangle

### Obtuse scalene triangle.

Sides: a = 5   b = 20   c = 23

Area: T = 42.70883130081
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 10.70112654404° = 10°42'5″ = 0.18767723161 rad
Angle ∠ B = β = 47.9666483062° = 47°57'59″ = 0.837717306 rad
Angle ∠ C = γ = 121.3322251498° = 121°19'56″ = 2.11876472775 rad

Height: ha = 17.08333252033
Height: hb = 4.27108313008
Height: hc = 3.71437663485

Median: ma = 21.40767746286
Median: mb = 13.30441346957
Median: mc = 8.95882364336

Inradius: r = 1.7879513042
Circumradius: R = 13.46334210415

Vertex coordinates: A[23; 0] B[0; 0] C[3.3487826087; 3.71437663485]
Centroid: CG[8.78326086957; 1.23879221162]
Coordinates of the circumscribed circle: U[11.5; -7.00109789416]
Coordinates of the inscribed circle: I[4; 1.7879513042]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.299873456° = 169°17'55″ = 0.18767723161 rad
∠ B' = β' = 132.0343516938° = 132°2'1″ = 0.837717306 rad
∠ C' = γ' = 58.66877485024° = 58°40'4″ = 2.11876472775 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    