# 10 13 14 triangle

### Acute scalene triangle.

Sides: a = 10   b = 13   c = 14

Area: T = 62.38553949254
Perimeter: p = 37
Semiperimeter: s = 18.5

Angle ∠ A = α = 43.27991752006° = 43°16'45″ = 0.75553641048 rad
Angle ∠ B = β = 63.02769449584° = 63°1'37″ = 1.1100027707 rad
Angle ∠ C = γ = 73.6943879841° = 73°41'38″ = 1.28662008418 rad

Height: ha = 12.47770789851
Height: hb = 9.59877530654
Height: hc = 8.91221992751

Median: ma = 12.5549900398
Median: mb = 10.28334819006
Median: mc = 9.24766210045

Inradius: r = 3.37221835095
Circumradius: R = 7.29333737222

Vertex coordinates: A[14; 0] B[0; 0] C[4.53657142857; 8.91221992751]
Centroid: CG[6.17985714286; 2.97107330917]
Coordinates of the circumscribed circle: U[7; 2.04877549297]
Coordinates of the inscribed circle: I[5.5; 3.37221835095]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.7210824799° = 136°43'15″ = 0.75553641048 rad
∠ B' = β' = 116.9733055042° = 116°58'23″ = 1.1100027707 rad
∠ C' = γ' = 106.3066120159° = 106°18'22″ = 1.28662008418 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    