# 12 19 19 triangle

### Acute isosceles triangle.

Sides: a = 12   b = 19   c = 19

Area: T = 108.1676538264
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 36.81769603412° = 36°49'1″ = 0.64325771785 rad
Angle ∠ B = β = 71.59215198294° = 71°35'29″ = 1.25495077375 rad
Angle ∠ C = γ = 71.59215198294° = 71°35'29″ = 1.25495077375 rad

Height: ha = 18.02877563773
Height: hb = 11.38659513962
Height: hc = 11.38659513962

Median: ma = 18.02877563773
Median: mb = 12.73877392029
Median: mc = 12.73877392029

Inradius: r = 4.32766615306
Circumradius: R = 10.01223385419

Vertex coordinates: A[19; 0] B[0; 0] C[3.78994736842; 11.38659513962]
Centroid: CG[7.59664912281; 3.79553171321]
Coordinates of the circumscribed circle: U[9.5; 3.16217911185]
Coordinates of the inscribed circle: I[6; 4.32766615306]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.1833039659° = 143°10'59″ = 0.64325771785 rad
∠ B' = β' = 108.4088480171° = 108°24'31″ = 1.25495077375 rad
∠ C' = γ' = 108.4088480171° = 108°24'31″ = 1.25495077375 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    