# 19 30 30 triangle

### Acute isosceles triangle.

Sides: a = 19   b = 30   c = 30

Area: T = 270.3333012227
Perimeter: p = 79
Semiperimeter: s = 39.5

Angle ∠ A = α = 36.92329165935° = 36°55'23″ = 0.6444426464 rad
Angle ∠ B = β = 71.53985417032° = 71°32'19″ = 1.24985830948 rad
Angle ∠ C = γ = 71.53985417032° = 71°32'19″ = 1.24985830948 rad

Height: ha = 28.45661065503
Height: hb = 18.02222008152
Height: hc = 18.02222008152

Median: ma = 28.45661065503
Median: mb = 20.13770305656
Median: mc = 20.13770305656

Inradius: r = 6.84438737273
Circumradius: R = 15.81438288949

Vertex coordinates: A[30; 0] B[0; 0] C[6.01766666667; 18.02222008152]
Centroid: CG[12.00655555556; 6.00774002717]
Coordinates of the circumscribed circle: U[15; 5.00877124834]
Coordinates of the inscribed circle: I[9.5; 6.84438737273]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.0777083406° = 143°4'37″ = 0.6444426464 rad
∠ B' = β' = 108.4611458297° = 108°27'41″ = 1.24985830948 rad
∠ C' = γ' = 108.4611458297° = 108°27'41″ = 1.24985830948 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    