# 11 13 14 triangle

### Acute scalene triangle.

Sides: a = 11   b = 13   c = 14

Area: T = 67.52877720645
Perimeter: p = 38
Semiperimeter: s = 19

Angle ∠ A = α = 47.90774859842° = 47°54'27″ = 0.83661433668 rad
Angle ∠ B = β = 61.28106643991° = 61°16'50″ = 1.07695493616 rad
Angle ∠ C = γ = 70.81218496167° = 70°48'43″ = 1.23658999252 rad

Height: ha = 12.2787776739
Height: hb = 10.38988880099
Height: hc = 9.64768245806

Median: ma = 12.33989626793
Median: mb = 10.78219293264
Median: mc = 9.79879589711

Inradius: r = 3.55440932666
Circumradius: R = 7.4121765333

Vertex coordinates: A[14; 0] B[0; 0] C[5.28657142857; 9.64768245806]
Centroid: CG[6.42985714286; 3.21656081935]
Coordinates of the circumscribed circle: U[7; 2.43660347598]
Coordinates of the inscribed circle: I[6; 3.55440932666]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.0932514016° = 132°5'33″ = 0.83661433668 rad
∠ B' = β' = 118.7199335601° = 118°43'10″ = 1.07695493616 rad
∠ C' = γ' = 109.1888150383° = 109°11'17″ = 1.23658999252 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    