# 17 20 24 triangle

### Acute scalene triangle.

Sides: a = 17   b = 20   c = 24

Area: T = 167.6366325121
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 44.30655563826° = 44°18'20″ = 0.77332778358 rad
Angle ∠ B = β = 55.26600284682° = 55°15'36″ = 0.96444694415 rad
Angle ∠ C = γ = 80.43444151492° = 80°26'4″ = 1.40438453763 rad

Height: ha = 19.72219206024
Height: hb = 16.76436325121
Height: hc = 13.97696937601

Median: ma = 20.39899485041
Median: mb = 18.23545825288
Median: mc = 14.16598022585

Inradius: r = 5.49662729548
Circumradius: R = 12.16992001929

Vertex coordinates: A[24; 0] B[0; 0] C[9.68875; 13.97696937601]
Centroid: CG[11.22991666667; 4.65765645867]
Coordinates of the circumscribed circle: U[12; 2.02222347379]
Coordinates of the inscribed circle: I[10.5; 5.49662729548]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.6944443617° = 135°41'40″ = 0.77332778358 rad
∠ B' = β' = 124.7439971532° = 124°44'24″ = 0.96444694415 rad
∠ C' = γ' = 99.56655848508° = 99°33'56″ = 1.40438453763 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    