4 17 19 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 17   c = 19

Area: T = 30.98438667697
Perimeter: p = 40
Semiperimeter: s = 20

Angle ∠ A = α = 11.06108009808° = 11°3'39″ = 0.1933047395 rad
Angle ∠ B = β = 54.62334598481° = 54°37'24″ = 0.95333592232 rad
Angle ∠ C = γ = 114.3165739171° = 114°18'57″ = 1.99551860354 rad

Height: ha = 15.49219333848
Height: hb = 3.64551607964
Height: hc = 3.261145966

Median: ma = 17.91664728672
Median: mb = 10.78219293264
Median: mc = 7.8989866919

Inradius: r = 1.54991933385
Circumradius: R = 10.42547801735

Vertex coordinates: A[19; 0] B[0; 0] C[2.31657894737; 3.261145966]
Centroid: CG[7.10552631579; 1.087715322]
Coordinates of the circumscribed circle: U[9.5; -4.2932556542]
Coordinates of the inscribed circle: I[3; 1.54991933385]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.9399199019° = 168°56'21″ = 0.1933047395 rad
∠ B' = β' = 125.3776540152° = 125°22'36″ = 0.95333592232 rad
∠ C' = γ' = 65.68442608288° = 65°41'3″ = 1.99551860354 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 = 4 ; ; b = 17 ; ; c = 19 ; ;

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

p = a+b+c = 4+17+19 = 40 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 40 }{ 2 } = 20 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20 * (20-4)(20-17)(20-19) } ; ; T = sqrt{ 960 } = 30.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 30.98 }{ 4 } = 15.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 30.98 }{ 17 } = 3.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 30.98 }{ 19 } = 3.26 ; ;

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{ 4**2-17**2-19**2 }{ 2 * 17 * 19 } ) = 11° 3'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-4**2-19**2 }{ 2 * 4 * 19 } ) = 54° 37'24" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-4**2-17**2 }{ 2 * 17 * 4 } ) = 114° 18'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 30.98 }{ 20 } = 1.55 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 11° 3'39" } = 10.42 ; ;




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