13 17 19 triangle

Acute scalene triangle.

Sides: a = 13   b = 17   c = 19

Area: T = 107.8066249819
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 41.87767878296° = 41°52'36″ = 0.73108878278 rad
Angle ∠ B = β = 60.88003549713° = 60°48'1″ = 1.06111663806 rad
Angle ∠ C = γ = 77.32328571991° = 77°19'22″ = 1.35495384452 rad

Height: ha = 16.58655768952
Height: hb = 12.6833088214
Height: hc = 11.34880262967

Median: ma = 16.81551717208
Median: mb = 13.88334433769
Median: mc = 11.77992189894

Vertex coordinates: A[19; 0] B[0; 0] C[6.34221052632; 11.34880262967]
Centroid: CG[8.44773684211; 3.78326754322]
Coordinates of the circumscribed circle: U[9.5; 2.13769354781]
Coordinates of the inscribed circle: I[7.5; 4.44002550946]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.123321217° = 138°7'24″ = 0.73108878278 rad
∠ B' = β' = 119.2199645029° = 119°11'59″ = 1.06111663806 rad
∠ C' = γ' = 102.6777142801° = 102°40'38″ = 1.35495384452 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    