# 18 26 27 triangle

### Acute scalene triangle.

Sides: a = 18   b = 26   c = 27

Area: T = 223.9787537936
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 39.65112276303° = 39°39'4″ = 0.69220444746 rad
Angle ∠ B = β = 67.17985871587° = 67°10'43″ = 1.17224875328 rad
Angle ∠ C = γ = 73.17701852111° = 73°10'13″ = 1.27770606462 rad

Height: ha = 24.8866393104
Height: hb = 17.22990413797
Height: hc = 16.5910928736

Median: ma = 24.93299017246
Median: mb = 18.90876704012
Median: mc = 17.826554347

Inradius: r = 6.30992264207
Circumradius: R = 14.10440928885

Vertex coordinates: A[27; 0] B[0; 0] C[6.98114814815; 16.5910928736]
Centroid: CG[11.32771604938; 5.53303095787]
Coordinates of the circumscribed circle: U[13.5; 4.08435568085]
Coordinates of the inscribed circle: I[9.5; 6.30992264207]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.349877237° = 140°20'56″ = 0.69220444746 rad
∠ B' = β' = 112.8211412841° = 112°49'17″ = 1.17224875328 rad
∠ C' = γ' = 106.8329814789° = 106°49'47″ = 1.27770606462 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    