# 12 14 21 triangle

### Obtuse scalene triangle.

Sides: a = 12   b = 14   c = 21

Area: T = 80.11551515008
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 33.02547340605° = 33°1'29″ = 0.5766390344 rad
Angle ∠ B = β = 39.48219079378° = 39°28'55″ = 0.68990892885 rad
Angle ∠ C = γ = 107.4933358002° = 107°29'36″ = 1.87661130212 rad

Height: ha = 13.35325252501
Height: hb = 11.4455021643
Height: hc = 7.63300144286

Median: ma = 16.8087736314
Median: mb = 15.60444865343
Median: mc = 7.73298124169

Inradius: r = 3.4099155383
Circumradius: R = 11.00991534932

Vertex coordinates: A[21; 0] B[0; 0] C[9.26219047619; 7.63300144286]
Centroid: CG[10.08773015873; 2.54333381429]
Coordinates of the circumscribed circle: U[10.5; -3.30992991155]
Coordinates of the inscribed circle: I[9.5; 3.4099155383]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.9755265939° = 146°58'31″ = 0.5766390344 rad
∠ B' = β' = 140.5188092062° = 140°31'5″ = 0.68990892885 rad
∠ C' = γ' = 72.50766419983° = 72°30'24″ = 1.87661130212 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    