# 6 24 27 triangle

### Obtuse scalene triangle.

Sides: a = 6   b = 24   c = 27

Area: T = 65.79108618275
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 11.71658523949° = 11°42'57″ = 0.2044480199 rad
Angle ∠ B = β = 54.31546652873° = 54°18'53″ = 0.94879697414 rad
Angle ∠ C = γ = 113.9699482318° = 113°58'10″ = 1.98991427132 rad

Height: ha = 21.93302872758
Height: hb = 5.4832571819
Height: hc = 4.87333971724

Median: ma = 25.36773017879
Median: mb = 15.44334452115
Median: mc = 11.12442977306

Inradius: r = 2.30884512922
Circumradius: R = 14.774408827

Vertex coordinates: A[27; 0] B[0; 0] C[3.5; 4.87333971724]
Centroid: CG[10.16766666667; 1.62444657241]
Coordinates of the circumscribed circle: U[13.5; -6.00219733597]
Coordinates of the inscribed circle: I[4.5; 2.30884512922]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.2844147605° = 168°17'3″ = 0.2044480199 rad
∠ B' = β' = 125.6855334713° = 125°41'7″ = 0.94879697414 rad
∠ C' = γ' = 66.03105176822° = 66°1'50″ = 1.98991427132 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    