# 21 22 23 triangle

### Acute scalene triangle.

Sides: a = 21   b = 22   c = 23

Area: T = 208.7110325571
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 55.58326112896° = 55°34'57″ = 0.97700995739 rad
Angle ∠ B = β = 59.79443222356° = 59°47'40″ = 1.0443607797 rad
Angle ∠ C = γ = 64.62330664748° = 64°37'23″ = 1.12878852827 rad

Height: ha = 19.87771738639
Height: hb = 18.9743665961
Height: hc = 18.14987239627

Median: ma = 19.90660292374
Median: mb = 19.07987840283
Median: mc = 18.17327818454

Inradius: r = 6.32545553203
Circumradius: R = 12.72881675822

Vertex coordinates: A[23; 0] B[0; 0] C[10.56552173913; 18.14987239627]
Centroid: CG[11.18884057971; 6.05495746542]
Coordinates of the circumscribed circle: U[11.5; 5.45549289638]
Coordinates of the inscribed circle: I[11; 6.32545553203]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 124.417738871° = 124°25'3″ = 0.97700995739 rad
∠ B' = β' = 120.2065677764° = 120°12'20″ = 1.0443607797 rad
∠ C' = γ' = 115.3776933525° = 115°22'37″ = 1.12878852827 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    