17 18 19 triangle

Acute scalene triangle.

Sides: a = 17   b = 18   c = 19

Area: T = 139.4277400463
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 54.62334598481° = 54°37'24″ = 0.95333592232 rad
Angle ∠ B = β = 59.69222793231° = 59°41'32″ = 1.04218268122 rad
Angle ∠ C = γ = 65.68442608288° = 65°41'3″ = 1.14664066182 rad

Height: ha = 16.40332235839
Height: hb = 15.49219333848
Height: hc = 14.67765684698

Median: ma = 16.43992822228
Median: mb = 15.62204993518
Median: mc = 14.70554411699

Inradius: r = 5.16439777949
Circumradius: R = 10.42547801735

Vertex coordinates: A[19; 0] B[0; 0] C[8.57989473684; 14.67765684698]
Centroid: CG[9.19329824561; 4.89221894899]
Coordinates of the circumscribed circle: U[9.5; 4.2932556542]
Coordinates of the inscribed circle: I[9; 5.16439777949]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.3776540152° = 125°22'36″ = 0.95333592232 rad
∠ B' = β' = 120.3087720677° = 120°18'28″ = 1.04218268122 rad
∠ C' = γ' = 114.3165739171° = 114°18'57″ = 1.14664066182 rad

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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.

a = 17 ; ; b = 18 ; ; c = 19 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 17+18+19 = 54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54 }{ 2 } = 27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27 * (27-17)(27-18)(27-19) } ; ; T = sqrt{ 19440 } = 139.43 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 139.43 }{ 17 } = 16.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 139.43 }{ 18 } = 15.49 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 139.43 }{ 19 } = 14.68 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 17**2-18**2-19**2 }{ 2 * 18 * 19 } ) = 54° 37'24" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-17**2-19**2 }{ 2 * 17 * 19 } ) = 59° 41'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-17**2-18**2 }{ 2 * 18 * 17 } ) = 65° 41'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 139.43 }{ 27 } = 5.16 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 54° 37'24" } = 10.42 ; ;




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