# 17 28 29 triangle

### Acute scalene triangle.

Sides: a = 17   b = 28   c = 29

Area: T = 230.825460874
Perimeter: p = 74
Semiperimeter: s = 37

Angle ∠ A = α = 34.64880267617° = 34°38'53″ = 0.60547221463 rad
Angle ∠ B = β = 69.45768450907° = 69°27'25″ = 1.21222506349 rad
Angle ∠ C = γ = 75.89551281476° = 75°53'42″ = 1.32546198724 rad

Height: ha = 27.15658363224
Height: hb = 16.48774720529
Height: hc = 15.91989385338

Median: ma = 27.20875357208
Median: mb = 19.20993727123
Median: mc = 18.06223918682

Inradius: r = 6.23985029389
Circumradius: R = 14.95107455849

Vertex coordinates: A[29; 0] B[0; 0] C[5.96655172414; 15.91989385338]
Centroid: CG[11.65551724138; 5.30663128446]
Coordinates of the circumscribed circle: U[14.5; 3.64334590081]
Coordinates of the inscribed circle: I[9; 6.23985029389]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.3521973238° = 145°21'7″ = 0.60547221463 rad
∠ B' = β' = 110.5433154909° = 110°32'35″ = 1.21222506349 rad
∠ C' = γ' = 104.1054871852° = 104°6'18″ = 1.32546198724 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    