12 19 27 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 19   c = 27

Area: T = 99.29875326985
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 22.77657191519° = 22°46'33″ = 0.39875112887 rad
Angle ∠ B = β = 37.80329497815° = 37°48'11″ = 0.66597859407 rad
Angle ∠ C = γ = 119.4211331067° = 119°25'17″ = 2.08442954242 rad

Height: ha = 16.55495887831
Height: hb = 10.4522371863
Height: hc = 7.35553727925

Median: ma = 22.56110283454
Median: mb = 18.60877940659
Median: mc = 8.38215273071

Vertex coordinates: A[27; 0] B[0; 0] C[9.48114814815; 7.35553727925]
Centroid: CG[12.16604938272; 2.45217909308]
Coordinates of the circumscribed circle: U[13.5; -7.61334822231]
Coordinates of the inscribed circle: I[10; 3.42440528517]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.2244280848° = 157°13'27″ = 0.39875112887 rad
∠ B' = β' = 142.1977050219° = 142°11'49″ = 0.66597859407 rad
∠ C' = γ' = 60.57986689334° = 60°34'43″ = 2.08442954242 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    