# 20 21 22 triangle

### Acute scalene triangle.

Sides: a = 20   b = 21   c = 22

Area: T = 190.0910603397
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 55.37664645208° = 55°22'35″ = 0.9676501634 rad
Angle ∠ B = β = 59.77441988917° = 59°46'27″ = 1.04332565784 rad
Angle ∠ C = γ = 64.84993365875° = 64°50'58″ = 1.13218344412 rad

Height: ha = 19.00990603397
Height: hb = 18.10438669902
Height: hc = 17.28109639452

Median: ma = 19.03994327647
Median: mb = 18.21440056001
Median: mc = 17.30660682999

Inradius: r = 6.03546223301
Circumradius: R = 12.15220998867

Vertex coordinates: A[22; 0] B[0; 0] C[10.06881818182; 17.28109639452]
Centroid: CG[10.68993939394; 5.76603213151]
Coordinates of the circumscribed circle: U[11; 5.16546424518]
Coordinates of the inscribed circle: I[10.5; 6.03546223301]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 124.6243535479° = 124°37'25″ = 0.9676501634 rad
∠ B' = β' = 120.2265801108° = 120°13'33″ = 1.04332565784 rad
∠ C' = γ' = 115.1510663413° = 115°9'2″ = 1.13218344412 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    