# 20 22 29 triangle

### Acute scalene triangle.

Sides: a = 20   b = 22   c = 29

Area: T = 219.7377200992
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 43.53876712285° = 43°32'16″ = 0.76598757116 rad
Angle ∠ B = β = 49.26331242172° = 49°15'47″ = 0.86598037174 rad
Angle ∠ C = γ = 87.19992045543° = 87°11'57″ = 1.52219132246 rad

Height: ha = 21.97437200992
Height: hb = 19.97661091811
Height: hc = 15.15442897236

Median: ma = 23.71770824513
Median: mb = 22.34994966386
Median: mc = 15.22333373476

Inradius: r = 6.19897803096
Circumradius: R = 14.51773415589

Vertex coordinates: A[29; 0] B[0; 0] C[13.05217241379; 15.15442897236]
Centroid: CG[14.01772413793; 5.05114299079]
Coordinates of the circumscribed circle: U[14.5; 0.70993700989]
Coordinates of the inscribed circle: I[13.5; 6.19897803096]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.4622328771° = 136°27'44″ = 0.76598757116 rad
∠ B' = β' = 130.7376875783° = 130°44'13″ = 0.86598037174 rad
∠ C' = γ' = 92.80107954457° = 92°48'3″ = 1.52219132246 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    