# 10 19 21 triangle

### Acute scalene triangle.

Sides: a = 10   b = 19   c = 21

Area: T = 94.86883298051
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 28.3943894835° = 28°23'38″ = 0.49655669523 rad
Angle ∠ B = β = 64.62330664748° = 64°37'23″ = 1.12878852827 rad
Angle ∠ C = γ = 86.98330386902° = 86°58'59″ = 1.51881404185 rad

Height: ha = 18.9743665961
Height: hb = 9.98661399795
Height: hc = 9.03550790291

Median: ma = 19.39107194297
Median: mb = 13.42657215821
Median: mc = 10.96658560997

Inradius: r = 3.79547331922
Circumradius: R = 10.51545732201

Vertex coordinates: A[21; 0] B[0; 0] C[4.28657142857; 9.03550790291]
Centroid: CG[8.42985714286; 3.01216930097]
Coordinates of the circumscribed circle: U[10.5; 0.55333985905]
Coordinates of the inscribed circle: I[6; 3.79547331922]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.6066105165° = 151°36'22″ = 0.49655669523 rad
∠ B' = β' = 115.3776933525° = 115°22'37″ = 1.12878852827 rad
∠ C' = γ' = 93.01769613098° = 93°1'1″ = 1.51881404185 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    