# 14 17 18 triangle

### Acute scalene triangle.

Sides: a = 14   b = 17   c = 18

Area: T = 111.986632729
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 47.04990078078° = 47°2'56″ = 0.8211160096 rad
Angle ∠ B = β = 62.7220387264° = 62°43'13″ = 1.09546772659 rad
Angle ∠ C = γ = 70.23106049282° = 70°13'50″ = 1.22657552917 rad

Height: ha = 15.99880467558
Height: hb = 13.17548620342
Height: hc = 12.44329252545

Median: ma = 16.04768065359
Median: mb = 13.7022189606
Median: mc = 12.70882650271

Inradius: r = 4.57108705017
Circumradius: R = 9.56436675111

Vertex coordinates: A[18; 0] B[0; 0] C[6.41766666667; 12.44329252545]
Centroid: CG[8.13988888889; 4.14876417515]
Coordinates of the circumscribed circle: U[9; 3.23547698935]
Coordinates of the inscribed circle: I[7.5; 4.57108705017]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.9510992192° = 132°57'4″ = 0.8211160096 rad
∠ B' = β' = 117.2879612736° = 117°16'47″ = 1.09546772659 rad
∠ C' = γ' = 109.7699395072° = 109°46'10″ = 1.22657552917 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    