# 16 22 23 triangle

### Acute scalene triangle.

Sides: a = 16   b = 22   c = 23

Area: T = 167.9099015541
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 41.58105251992° = 41°34'50″ = 0.72657170694 rad
Angle ∠ B = β = 65.86600155707° = 65°51'36″ = 1.14994741171 rad
Angle ∠ C = γ = 72.55994592301° = 72°33'34″ = 1.2666401467 rad

Height: ha = 20.98986269426
Height: hb = 15.26444559583
Height: hc = 14.60107839601

Median: ma = 21.0365683968
Median: mb = 16.47772570533
Median: mc = 15.41991439451

Inradius: r = 5.50552136243
Circumradius: R = 12.05441472623

Vertex coordinates: A[23; 0] B[0; 0] C[6.54334782609; 14.60107839601]
Centroid: CG[9.8487826087; 4.86769279867]
Coordinates of the circumscribed circle: U[11.5; 3.6132819705]
Coordinates of the inscribed circle: I[8.5; 5.50552136243]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.4199474801° = 138°25'10″ = 0.72657170694 rad
∠ B' = β' = 114.1439984429° = 114°8'24″ = 1.14994741171 rad
∠ C' = γ' = 107.441054077° = 107°26'26″ = 1.2666401467 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    