# 18 19 23 triangle

### Acute scalene triangle.

Sides: a = 18   b = 19   c = 23

Area: T = 166.4933243106
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 49.6399310869° = 49°38'22″ = 0.86663694131 rad
Angle ∠ B = β = 53.54441706172° = 53°32'39″ = 0.93545220725 rad
Angle ∠ C = γ = 76.81765185138° = 76°48'59″ = 1.3410701168 rad

Height: ha = 18.4999249234
Height: hb = 17.52656045375
Height: hc = 14.47876733136

Median: ma = 19.07987840283
Median: mb = 18.33771208209
Median: mc = 14.5

Inradius: r = 5.55497747702
Circumradius: R = 11.81112901359

Vertex coordinates: A[23; 0] B[0; 0] C[10.69656521739; 14.47876733136]
Centroid: CG[11.2321884058; 4.82658911045]
Coordinates of the circumscribed circle: U[11.5; 2.69438030135]
Coordinates of the inscribed circle: I[11; 5.55497747702]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.3610689131° = 130°21'38″ = 0.86663694131 rad
∠ B' = β' = 126.4565829383° = 126°27'21″ = 0.93545220725 rad
∠ C' = γ' = 103.1833481486° = 103°11'1″ = 1.3410701168 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    