11 12 19 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 12   c = 19

Area: T = 61.48217045958
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 32.63768975036° = 32°38'13″ = 0.57696213191 rad
Angle ∠ B = β = 36.03994162329° = 36°2'22″ = 0.62990064738 rad
Angle ∠ C = γ = 111.3243686263° = 111°19'25″ = 1.94329648608 rad

Height: ha = 11.17884917447
Height: hb = 10.2476950766
Height: hc = 6.47217583785

Median: ma = 14.90880515159
Median: mb = 14.31878210633
Median: mc = 6.5

Inradius: r = 2.92877002188
Circumradius: R = 10.19881557623

Vertex coordinates: A[19; 0] B[0; 0] C[8.89547368421; 6.47217583785]
Centroid: CG[9.2988245614; 2.15772527928]
Coordinates of the circumscribed circle: U[9.5; -3.70884202772]
Coordinates of the inscribed circle: I[9; 2.92877002188]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.3633102496° = 147°21'47″ = 0.57696213191 rad
∠ B' = β' = 143.9610583767° = 143°57'38″ = 0.62990064738 rad
∠ C' = γ' = 68.67663137365° = 68°40'35″ = 1.94329648608 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 = 11 ; ; b = 12 ; ; c = 19 ; ;

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

p = a+b+c = 11+12+19 = 42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 42 }{ 2 } = 21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21 * (21-11)(21-12)(21-19) } ; ; T = sqrt{ 3780 } = 61.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 61.48 }{ 11 } = 11.18 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 61.48 }{ 12 } = 10.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 61.48 }{ 19 } = 6.47 ; ;

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{ 11**2-12**2-19**2 }{ 2 * 12 * 19 } ) = 32° 38'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-11**2-19**2 }{ 2 * 11 * 19 } ) = 36° 2'22" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-11**2-12**2 }{ 2 * 12 * 11 } ) = 111° 19'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 61.48 }{ 21 } = 2.93 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 32° 38'13" } = 10.2 ; ;




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