19 23 24 triangle

Acute scalene triangle.

Sides: a = 19   b = 23   c = 24

Area: T = 203.9121745616
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 47.63302014306° = 47°37'49″ = 0.83113038384 rad
Angle ∠ B = β = 63.4255030481° = 63°25'30″ = 1.10769756101 rad
Angle ∠ C = γ = 68.94547680884° = 68°56'41″ = 1.20333132052 rad

Height: ha = 21.46443942753
Height: hb = 17.73114561405
Height: hc = 16.9932645468

Median: ma = 21.5
Median: mb = 18.33771208209
Median: mc = 17.34993515729

Vertex coordinates: A[24; 0] B[0; 0] C[8.5; 16.9932645468]
Centroid: CG[10.83333333333; 5.6644215156]
Coordinates of the circumscribed circle: U[12; 4.62196456077]
Coordinates of the inscribed circle: I[10; 6.17991438065]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.3769798569° = 132°22'11″ = 0.83113038384 rad
∠ B' = β' = 116.5754969519° = 116°34'30″ = 1.10769756101 rad
∠ C' = γ' = 111.0555231912° = 111°3'19″ = 1.20333132052 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    