# 11 18 20 triangle

### Acute scalene triangle.

Sides: a = 11   b = 18   c = 20

Area: T = 98.35987184748
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 33.12329402077° = 33°7'23″ = 0.57881043646 rad
Angle ∠ B = β = 63.40220386364° = 63°24'7″ = 1.10765743267 rad
Angle ∠ C = γ = 83.47550211559° = 83°28'30″ = 1.45769139623 rad

Height: ha = 17.88334033591
Height: hb = 10.92987464972
Height: hc = 9.83658718475

Median: ma = 18.21440056001
Median: mb = 13.3987761007
Median: mc = 11.06879718106

Inradius: r = 4.01546415704
Circumradius: R = 10.06551982392

Vertex coordinates: A[20; 0] B[0; 0] C[4.925; 9.83658718475]
Centroid: CG[8.30883333333; 3.27986239492]
Coordinates of the circumscribed circle: U[10; 1.14437725272]
Coordinates of the inscribed circle: I[6.5; 4.01546415704]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.8777059792° = 146°52'37″ = 0.57881043646 rad
∠ B' = β' = 116.5987961364° = 116°35'53″ = 1.10765743267 rad
∠ C' = γ' = 96.52549788441° = 96°31'30″ = 1.45769139623 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    