# 12 19 22 triangle

### Acute scalene triangle.

Sides: a = 12   b = 19   c = 22

Area: T = 113.8799047678
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 33.01661784386° = 33°58″ = 0.57662410202 rad
Angle ∠ B = β = 59.62333765621° = 59°37'24″ = 1.04106242322 rad
Angle ∠ C = γ = 87.36604449993° = 87°21'38″ = 1.52547274012 rad

Height: ha = 18.98798412796
Height: hb = 11.98772681766
Height: hc = 10.3532640698

Median: ma = 19.66596032513
Median: mb = 14.95882753017
Median: mc = 11.46773449412

Inradius: r = 4.29773225539
Circumradius: R = 11.01216832338

Vertex coordinates: A[22; 0] B[0; 0] C[6.06881818182; 10.3532640698]
Centroid: CG[9.35660606061; 3.45108802327]
Coordinates of the circumscribed circle: U[11; 0.5077116991]
Coordinates of the inscribed circle: I[7.5; 4.29773225539]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.9843821561° = 146°59'2″ = 0.57662410202 rad
∠ B' = β' = 120.3776623438° = 120°22'36″ = 1.04106242322 rad
∠ C' = γ' = 92.64395550007° = 92°38'22″ = 1.52547274012 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    