# 17 21 23 triangle

### Acute scalene triangle.

Sides: a = 17   b = 21   c = 23

Area: T = 171.2811019088
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 45.17329648542° = 45°10'23″ = 0.78884169696 rad
Angle ∠ B = β = 61.17875376083° = 61°10'39″ = 1.06877494595 rad
Angle ∠ C = γ = 73.64994975375° = 73°38'58″ = 1.28554262245 rad

Height: ha = 20.15107081281
Height: hb = 16.31224780084
Height: hc = 14.89440016599

Median: ma = 20.31662496539
Median: mb = 17.28443860174
Median: mc = 15.25661463024

Inradius: r = 5.61657711177
Circumradius: R = 11.98546904866

Vertex coordinates: A[23; 0] B[0; 0] C[8.19656521739; 14.89440016599]
Centroid: CG[10.39985507246; 4.965466722]
Coordinates of the circumscribed circle: U[11.5; 3.37438414395]
Coordinates of the inscribed circle: I[9.5; 5.61657711177]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.8277035146° = 134°49'37″ = 0.78884169696 rad
∠ B' = β' = 118.8222462392° = 118°49'21″ = 1.06877494595 rad
∠ C' = γ' = 106.3510502463° = 106°21'2″ = 1.28554262245 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    