# 12 15 19 triangle

### Acute scalene triangle.

Sides: a = 12   b = 15   c = 19

Area: T = 89.97877750336
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 39.15551858195° = 39°9'19″ = 0.68333869118 rad
Angle ∠ B = β = 52.11881585419° = 52°7'5″ = 0.91096334666 rad
Angle ∠ C = γ = 88.72766556386° = 88°43'36″ = 1.54985722752 rad

Height: ha = 14.99662958389
Height: hb = 11.99770366711
Height: hc = 9.47113447404

Median: ma = 16.03112195419
Median: mb = 14.00989257261
Median: mc = 9.70882439195

Inradius: r = 3.91220771754
Circumradius: R = 9.50223465481

Vertex coordinates: A[19; 0] B[0; 0] C[7.36884210526; 9.47113447404]
Centroid: CG[8.78994736842; 3.15771149135]
Coordinates of the circumscribed circle: U[9.5; 0.21111632566]
Coordinates of the inscribed circle: I[8; 3.91220771754]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.845481418° = 140°50'41″ = 0.68333869118 rad
∠ B' = β' = 127.8821841458° = 127°52'55″ = 0.91096334666 rad
∠ C' = γ' = 91.27333443614° = 91°16'24″ = 1.54985722752 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    