8 13 19 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 13   c = 19

Area: T = 40.98878030638
Perimeter: p = 40
Semiperimeter: s = 20

Angle ∠ A = α = 19.38332300516° = 19°23' = 0.33883011841 rad
Angle ∠ B = β = 32.63768975036° = 32°38'13″ = 0.57696213191 rad
Angle ∠ C = γ = 127.9879872445° = 127°58'48″ = 2.23436701504 rad

Height: ha = 10.2476950766
Height: hb = 6.3065815856
Height: hc = 4.31545055857

Median: ma = 15.78797338381
Median: mb = 13.04879883507
Median: mc = 5.1233475383

Inradius: r = 2.04993901532
Circumradius: R = 12.05223659009

Vertex coordinates: A[19; 0] B[0; 0] C[6.73768421053; 4.31545055857]
Centroid: CG[8.57989473684; 1.43881685286]
Coordinates of the circumscribed circle: U[9.5; -7.41768405544]
Coordinates of the inscribed circle: I[7; 2.04993901532]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.6176769948° = 160°37' = 0.33883011841 rad
∠ B' = β' = 147.3633102496° = 147°21'47″ = 0.57696213191 rad
∠ C' = γ' = 52.02201275551° = 52°1'12″ = 2.23436701504 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 = 8 ; ; b = 13 ; ; c = 19 ; ;

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

p = a+b+c = 8+13+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 * (20-8)(20-13)(20-19) } ; ; T = sqrt{ 1680 } = 40.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 40.99 }{ 8 } = 10.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 40.99 }{ 13 } = 6.31 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 40.99 }{ 19 } = 4.31 ; ;

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{ 8**2-13**2-19**2 }{ 2 * 13 * 19 } ) = 19° 23' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-8**2-19**2 }{ 2 * 8 * 19 } ) = 32° 38'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-8**2-13**2 }{ 2 * 13 * 8 } ) = 127° 58'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 40.99 }{ 20 } = 2.05 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 19° 23' } = 12.05 ; ;




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