# 17 19 24 triangle

### Acute scalene triangle.

Sides: a = 17   b = 19   c = 24

Area: T = 160.4376903486
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 44.72222460248° = 44°43'20″ = 0.7810550442 rad
Angle ∠ B = β = 51.85554868988° = 51°51'20″ = 0.90550489816 rad
Angle ∠ C = γ = 83.42222670764° = 83°25'20″ = 1.456599323 rad

Height: ha = 18.87549298218
Height: hb = 16.88880951037
Height: hc = 13.37697419571

Median: ma = 19.90660292374
Median: mb = 18.5
Median: mc = 13.45436240471

Inradius: r = 5.34878967828
Circumradius: R = 12.08795151109

Vertex coordinates: A[24; 0] B[0; 0] C[10.5; 13.37697419571]
Centroid: CG[11.5; 4.45765806524]
Coordinates of the circumscribed circle: U[12; 1.38437215452]
Coordinates of the inscribed circle: I[11; 5.34878967828]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.2787753975° = 135°16'40″ = 0.7810550442 rad
∠ B' = β' = 128.1454513101° = 128°8'40″ = 0.90550489816 rad
∠ C' = γ' = 96.57877329236° = 96°34'40″ = 1.456599323 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    