# 12 14 20 triangle

### Obtuse scalene triangle.

Sides: a = 12   b = 14   c = 20

Area: T = 82.65498638837
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 36.18222872212° = 36°10'56″ = 0.63215000429 rad
Angle ∠ B = β = 43.53111521674° = 43°31'52″ = 0.76597619325 rad
Angle ∠ C = γ = 100.2876560611° = 100°17'12″ = 1.75503306782 rad

Height: ha = 13.7754977314
Height: hb = 11.8077123412
Height: hc = 8.26549863884

Median: ma = 16.18664140562
Median: mb = 14.93331845231
Median: mc = 8.36766002653

Inradius: r = 3.59334723428
Circumradius: R = 10.1633356121

Vertex coordinates: A[20; 0] B[0; 0] C[8.7; 8.26549863884]
Centroid: CG[9.56766666667; 2.75549954628]
Coordinates of the circumscribed circle: U[10; -1.81548850216]
Coordinates of the inscribed circle: I[9; 3.59334723428]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.8187712779° = 143°49'4″ = 0.63215000429 rad
∠ B' = β' = 136.4698847833° = 136°28'8″ = 0.76597619325 rad
∠ C' = γ' = 79.71334393885° = 79°42'48″ = 1.75503306782 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    