10 11 12 triangle

Acute scalene triangle.

Sides: a = 10   b = 11   c = 12

Area: T = 51.52112334868
Perimeter: p = 33
Semiperimeter: s = 16.5

Angle ∠ A = α = 51.31878125465° = 51°19'4″ = 0.89656647939 rad
Angle ∠ B = β = 59.17695025682° = 59°10'10″ = 1.03327026366 rad
Angle ∠ C = γ = 69.51326848853° = 69°30'46″ = 1.21332252231 rad

Height: ha = 10.30442466974
Height: hb = 9.36774969976
Height: hc = 8.58768722478

Median: ma = 10.36882206767
Median: mb = 9.57986220303
Median: mc = 8.63113382508

Vertex coordinates: A[12; 0] B[0; 0] C[5.125; 8.58768722478]
Centroid: CG[5.70883333333; 2.86222907493]
Coordinates of the circumscribed circle: U[6; 2.24217941533]
Coordinates of the inscribed circle: I[5.5; 3.12224989992]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.6822187453° = 128°40'56″ = 0.89656647939 rad
∠ B' = β' = 120.8330497432° = 120°49'50″ = 1.03327026366 rad
∠ C' = γ' = 110.4877315115° = 110°29'14″ = 1.21332252231 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    