# 3 20 21 triangle

### Obtuse scalene triangle.

Sides: a = 3   b = 20   c = 21

Area: T = 28.91436645896
Perimeter: p = 44
Semiperimeter: s = 22

Angle ∠ A = α = 7.91438581623° = 7°54'50″ = 0.13881228815 rad
Angle ∠ B = β = 66.62201318843° = 66°37'12″ = 1.16327406495 rad
Angle ∠ C = γ = 105.4666009953° = 105°27'58″ = 1.84107291226 rad

Height: ha = 19.27657763931
Height: hb = 2.8911366459
Height: hc = 2.75436823419

Median: ma = 20.45111613362
Median: mb = 11.18803398875
Median: mc = 9.70882439195

Inradius: r = 1.31442574813
Circumradius: R = 10.89545028059

Vertex coordinates: A[21; 0] B[0; 0] C[1.19904761905; 2.75436823419]
Centroid: CG[7.39768253968; 0.9187894114]
Coordinates of the circumscribed circle: U[10.5; -2.90552007482]
Coordinates of the inscribed circle: I[2; 1.31442574813]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 172.0866141838° = 172°5'10″ = 0.13881228815 rad
∠ B' = β' = 113.3879868116° = 113°22'48″ = 1.16327406495 rad
∠ C' = γ' = 74.53439900466° = 74°32'2″ = 1.84107291226 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    