# 19 20 21 triangle

### Acute scalene triangle.

Sides: a = 19   b = 20   c = 21

Area: T = 172.3376879396
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 55.1550095421° = 55°9' = 0.96325507479 rad
Angle ∠ B = β = 59.75109669494° = 59°45'3″ = 1.04328511045 rad
Angle ∠ C = γ = 65.09989376296° = 65°5'56″ = 1.13661908012 rad

Height: ha = 18.1410724147
Height: hb = 17.23436879396
Height: hc = 16.4133036133

Median: ma = 18.17327818454
Median: mb = 17.34993515729
Median: mc = 16.43992822228

Inradius: r = 5.74545626465
Circumradius: R = 11.57661641211

Vertex coordinates: A[21; 0] B[0; 0] C[9.57114285714; 16.4133036133]
Centroid: CG[10.19904761905; 5.47110120443]
Coordinates of the circumscribed circle: U[10.5; 4.87441743668]
Coordinates of the inscribed circle: I[10; 5.74545626465]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 124.8549904579° = 124°51' = 0.96325507479 rad
∠ B' = β' = 120.2499033051° = 120°14'57″ = 1.04328511045 rad
∠ C' = γ' = 114.901106237° = 114°54'4″ = 1.13661908012 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    