# 21 25 29 triangle

### Acute scalene triangle.

Sides: a = 21   b = 25   c = 29

Area: T = 256.402239371
Perimeter: p = 75
Semiperimeter: s = 37.5

Angle ∠ A = α = 45.01770320401° = 45°1'1″ = 0.78656954286 rad
Angle ∠ B = β = 57.35765930761° = 57°21'24″ = 1.00110613969 rad
Angle ∠ C = γ = 77.62663748838° = 77°37'35″ = 1.35548358281 rad

Height: ha = 24.41992755914
Height: hb = 20.51221914968
Height: hc = 17.68329237041

Median: ma = 24.95549594269
Median: mb = 22.01770388563
Median: mc = 17.96552442232

Inradius: r = 6.83773971656
Circumradius: R = 14.84548302098

Vertex coordinates: A[29; 0] B[0; 0] C[11.32875862069; 17.68329237041]
Centroid: CG[13.44325287356; 5.89443079014]
Coordinates of the circumscribed circle: U[14.5; 3.1811035045]
Coordinates of the inscribed circle: I[12.5; 6.83773971656]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.983296796° = 134°58'59″ = 0.78656954286 rad
∠ B' = β' = 122.6433406924° = 122°38'36″ = 1.00110613969 rad
∠ C' = γ' = 102.3743625116° = 102°22'25″ = 1.35548358281 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    