# 11 14 20 triangle

### Obtuse scalene triangle.

Sides: a = 11   b = 14   c = 20

Area: T = 74.15114497498
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 31.98220267884° = 31°58'55″ = 0.55881916689 rad
Angle ∠ B = β = 42.38546161308° = 42°23'5″ = 0.74397511037 rad
Angle ∠ C = γ = 105.6333357081° = 105°38' = 1.8443649881 rad

Height: ha = 13.48220817727
Height: hb = 10.593306425
Height: hc = 7.4155144975

Median: ma = 16.3633068172
Median: mb = 14.54330395722
Median: mc = 7.64985292704

Inradius: r = 3.29656199889
Circumradius: R = 10.38441530084

Vertex coordinates: A[20; 0] B[0; 0] C[8.125; 7.4155144975]
Centroid: CG[9.375; 2.47217149917]
Coordinates of the circumscribed circle: U[10; -2.79883269471]
Coordinates of the inscribed circle: I[8.5; 3.29656199889]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.0187973212° = 148°1'5″ = 0.55881916689 rad
∠ B' = β' = 137.6155383869° = 137°36'55″ = 0.74397511037 rad
∠ C' = γ' = 74.36766429192° = 74°22' = 1.8443649881 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    