# 13 18 18 triangle

### Acute isosceles triangle.

Sides: a = 13   b = 18   c = 18

Area: T = 109.1055167155
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 42.33768976917° = 42°20'13″ = 0.73989182598 rad
Angle ∠ B = β = 68.83215511542° = 68°49'54″ = 1.20113371969 rad
Angle ∠ C = γ = 68.83215511542° = 68°49'54″ = 1.20113371969 rad

Height: ha = 16.78554103316
Height: hb = 12.12327963506
Height: hc = 12.12327963506

Median: ma = 16.78554103316
Median: mb = 12.86546803303
Median: mc = 12.86546803303

Inradius: r = 4.45332721288
Circumradius: R = 9.65112385935

Vertex coordinates: A[18; 0] B[0; 0] C[4.69444444444; 12.12327963506]
Centroid: CG[7.56548148148; 4.04109321169]
Coordinates of the circumscribed circle: U[9; 3.48551694921]
Coordinates of the inscribed circle: I[6.5; 4.45332721288]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.6633102308° = 137°39'47″ = 0.73989182598 rad
∠ B' = β' = 111.1688448846° = 111°10'6″ = 1.20113371969 rad
∠ C' = γ' = 111.1688448846° = 111°10'6″ = 1.20113371969 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    