12 21 28 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 21   c = 28

Area: T = 115.762241834
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 23.18880202295° = 23°11'17″ = 0.40547073 rad
Angle ∠ B = β = 43.55659049333° = 43°33'21″ = 0.76601939498 rad
Angle ∠ C = γ = 113.2566074837° = 113°15'22″ = 1.97766914038 rad

Height: ha = 19.29437363901
Height: hb = 11.02549922229
Height: hc = 8.26987441672

Median: ma = 24.01104144071
Median: mb = 18.80882428738
Median: mc = 9.82334413522

Vertex coordinates: A[28; 0] B[0; 0] C[8.69664285714; 8.26987441672]
Centroid: CG[12.23221428571; 2.75662480557]
Coordinates of the circumscribed circle: U[14; -6.01766331179]
Coordinates of the inscribed circle: I[9.5; 3.79554891259]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.8121979771° = 156°48'43″ = 0.40547073 rad
∠ B' = β' = 136.4444095067° = 136°26'39″ = 0.76601939498 rad
∠ C' = γ' = 66.74439251627° = 66°44'38″ = 1.97766914038 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    