# 8 13 20 triangle

### Obtuse scalene triangle.

Sides: a = 8   b = 13   c = 20

Area: T = 30.99989919191
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 13.79552993996° = 13°47'43″ = 0.24107733958 rad
Angle ∠ B = β = 22.79882480997° = 22°47'54″ = 0.3987904493 rad
Angle ∠ C = γ = 143.4066452501° = 143°24'23″ = 2.50329147647 rad

Height: ha = 7.75497479798
Height: hb = 4.76990756799
Height: hc = 3.10998991919

Median: ma = 16.38659696082
Median: mb = 13.7754977314
Median: mc = 4.06220192023

Inradius: r = 1.51221459473
Circumradius: R = 16.77547390417

Vertex coordinates: A[20; 0] B[0; 0] C[7.375; 3.10998991919]
Centroid: CG[9.125; 1.03332997306]
Coordinates of the circumscribed circle: U[10; -13.46881799037]
Coordinates of the inscribed circle: I[7.5; 1.51221459473]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.20547006° = 166°12'17″ = 0.24107733958 rad
∠ B' = β' = 157.20217519° = 157°12'6″ = 0.3987904493 rad
∠ C' = γ' = 36.59435474993° = 36°35'37″ = 2.50329147647 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    