# 8 28 29 triangle

### Acute scalene triangle.

Sides: a = 8   b = 28   c = 29

Area: T = 111.986632729
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 16.01113870121° = 16°41″ = 0.27994514212 rad
Angle ∠ B = β = 74.88438959745° = 74°53'2″ = 1.30769705415 rad
Angle ∠ C = γ = 89.10547170134° = 89°6'17″ = 1.55551706909 rad

Height: ha = 27.99765818226
Height: hb = 7.99990233779
Height: hc = 7.72331949855

Median: ma = 28.22223315833
Median: mb = 16.0165617378
Median: mc = 14.62201915172

Inradius: r = 3.44657331474
Circumradius: R = 14.50217703437

Vertex coordinates: A[29; 0] B[0; 0] C[2.08662068966; 7.72331949855]
Centroid: CG[10.36220689655; 2.57443983285]
Coordinates of the circumscribed circle: U[14.5; 0.22765901616]
Coordinates of the inscribed circle: I[4.5; 3.44657331474]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.9898612988° = 163°59'19″ = 0.27994514212 rad
∠ B' = β' = 105.1166104025° = 105°6'58″ = 1.30769705415 rad
∠ C' = γ' = 90.89552829866° = 90°53'43″ = 1.55551706909 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    