# 14 21 23 triangle

### Acute scalene triangle.

Sides: a = 14   b = 21   c = 23

Area: T = 144.4999134946
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 36.75111085714° = 36°45'4″ = 0.64114278483 rad
Angle ∠ B = β = 63.83326940251° = 63°49'58″ = 1.11440906812 rad
Angle ∠ C = γ = 79.41661974035° = 79°24'58″ = 1.38660741241 rad

Height: ha = 20.64327335636
Height: hb = 13.76218223758
Height: hc = 12.56551421692

Median: ma = 20.88106130178
Median: mb = 15.88223801743
Median: mc = 13.6477344064

Inradius: r = 4.98327287912
Circumradius: R = 11.69990319744

Vertex coordinates: A[23; 0] B[0; 0] C[6.17439130435; 12.56551421692]
Centroid: CG[9.72546376812; 4.18883807231]
Coordinates of the circumscribed circle: U[11.5; 2.14988017912]
Coordinates of the inscribed circle: I[8; 4.98327287912]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.2498891429° = 143°14'56″ = 0.64114278483 rad
∠ B' = β' = 116.1677305975° = 116°10'2″ = 1.11440906812 rad
∠ C' = γ' = 100.5843802597° = 100°35'2″ = 1.38660741241 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    