# 5 16 20 triangle

### Obtuse scalene triangle.

Sides: a = 5   b = 16   c = 20

Area: T = 26.7388315205
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 9.62200904201° = 9°37'12″ = 0.16879022522 rad
Angle ∠ B = β = 32.32880641222° = 32°19'41″ = 0.56442311597 rad
Angle ∠ C = γ = 138.0521845458° = 138°3'7″ = 2.40994592417 rad

Height: ha = 10.6955326082
Height: hb = 3.34222894006
Height: hc = 2.67438315205

Median: ma = 17.93773911147
Median: mb = 12.1866057607
Median: mc = 6.36439610307

Inradius: r = 1.30443080588
Circumradius: R = 14.96598056921

Vertex coordinates: A[20; 0] B[0; 0] C[4.225; 2.67438315205]
Centroid: CG[8.075; 0.89112771735]
Coordinates of the circumscribed circle: U[10; -11.12663554835]
Coordinates of the inscribed circle: I[4.5; 1.30443080588]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.387990958° = 170°22'48″ = 0.16879022522 rad
∠ B' = β' = 147.6721935878° = 147°40'19″ = 0.56442311597 rad
∠ C' = γ' = 41.94881545423° = 41°56'53″ = 2.40994592417 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    