13 20 23 triangle

Acute scalene triangle.

Sides: a = 13   b = 20   c = 23

Area: T = 129.6154813968
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 34.30111527568° = 34°18'4″ = 0.59986680528 rad
Angle ∠ B = β = 60.1110573029° = 60°6'38″ = 1.04991274146 rad
Angle ∠ C = γ = 85.58882742142° = 85°35'18″ = 1.49437971861 rad

Height: ha = 19.94107406105
Height: hb = 12.96114813968
Height: hc = 11.27108533885

Median: ma = 20.5498722588
Median: mb = 15.78797338381
Median: mc = 12.33989626793

Vertex coordinates: A[23; 0] B[0; 0] C[6.47882608696; 11.27108533885]
Centroid: CG[9.82660869565; 3.75769511295]
Coordinates of the circumscribed circle: U[11.5; 0.88772442623]
Coordinates of the inscribed circle: I[8; 4.62991004989]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.6998847243° = 145°41'56″ = 0.59986680528 rad
∠ B' = β' = 119.8899426971° = 119°53'22″ = 1.04991274146 rad
∠ C' = γ' = 94.41217257858° = 94°24'42″ = 1.49437971861 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    