8 12 19 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 12   c = 19

Area: T = 28.99989223938
Perimeter: p = 39
Semiperimeter: s = 19.5

Angle ∠ A = α = 14.73766437225° = 14°44'12″ = 0.25772029537 rad
Angle ∠ B = β = 22.43106417388° = 22°25'50″ = 0.39114885517 rad
Angle ∠ C = γ = 142.8332714539° = 142°49'58″ = 2.49329011483 rad

Height: ha = 7.25497305984
Height: hb = 4.83331537323
Height: hc = 3.05325181467

Median: ma = 15.37985564992
Median: mb = 13.28553302556
Median: mc = 3.70880992435

Inradius: r = 1.48771242253
Circumradius: R = 15.72547222434

Vertex coordinates: A[19; 0] B[0; 0] C[7.39547368421; 3.05325181467]
Centroid: CG[8.7988245614; 1.01875060489]
Coordinates of the circumscribed circle: U[9.5; -12.53106380377]
Coordinates of the inscribed circle: I[7.5; 1.48771242253]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.2633356278° = 165°15'48″ = 0.25772029537 rad
∠ B' = β' = 157.5699358261° = 157°34'10″ = 0.39114885517 rad
∠ C' = γ' = 37.16772854613° = 37°10'2″ = 2.49329011483 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 = 12 ; ; c = 19 ; ;

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

p = a+b+c = 8+12+19 = 39 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 39 }{ 2 } = 19.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.5 * (19.5-8)(19.5-12)(19.5-19) } ; ; T = sqrt{ 840.94 } = 29 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 29 }{ 8 } = 7.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 29 }{ 12 } = 4.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 29 }{ 19 } = 3.05 ; ;

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**2-12**2-19**2 }{ 2 * 12 * 19 } ) = 14° 44'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-8**2-19**2 }{ 2 * 8 * 19 } ) = 22° 25'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-8**2-12**2 }{ 2 * 12 * 8 } ) = 142° 49'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 29 }{ 19.5 } = 1.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 14° 44'12" } = 15.72 ; ;




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