# 5 12 14 triangle

### Obtuse scalene triangle.

Sides: a = 5   b = 12   c = 14

Area: T = 29.23107629049
Perimeter: p = 31
Semiperimeter: s = 15.5

Angle ∠ A = α = 20.36441348063° = 20°21'51″ = 0.35554212017 rad
Angle ∠ B = β = 56.63329870308° = 56°37'59″ = 0.98884320889 rad
Angle ∠ C = γ = 103.0032878163° = 103°10″ = 1.7987739363 rad

Height: ha = 11.69223051619
Height: hb = 4.87217938175
Height: hc = 4.17658232721

Median: ma = 12.79664838921
Median: mb = 8.63113382508
Median: mc = 5.95881876439

Inradius: r = 1.88658556713
Circumradius: R = 7.18442120811

Vertex coordinates: A[14; 0] B[0; 0] C[2.75; 4.17658232721]
Centroid: CG[5.58333333333; 1.39219410907]
Coordinates of the circumscribed circle: U[7; -1.61664477182]
Coordinates of the inscribed circle: I[3.5; 1.88658556713]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.6365865194° = 159°38'9″ = 0.35554212017 rad
∠ B' = β' = 123.3677012969° = 123°22'1″ = 0.98884320889 rad
∠ C' = γ' = 76.99771218371° = 76°59'50″ = 1.7987739363 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    