9 19 27 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 19   c = 27

Area: T = 46.49993279521
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 10.4454554006° = 10°26'40″ = 0.18222918563 rad
Angle ∠ B = β = 22.50216797743° = 22°30'6″ = 0.39327283993 rad
Angle ∠ C = γ = 147.054376622° = 147°3'14″ = 2.5676572398 rad

Height: ha = 10.33331839894
Height: hb = 4.89546661002
Height: hc = 3.44443946631

Median: ma = 22.90774223779
Median: mb = 17.74111949992
Median: mc = 6.2254949799

Inradius: r = 1.69108846528
Circumradius: R = 24.82329394022

Vertex coordinates: A[27; 0] B[0; 0] C[8.31548148148; 3.44443946631]
Centroid: CG[11.77216049383; 1.14881315544]
Coordinates of the circumscribed circle: U[13.5; -20.83109462235]
Coordinates of the inscribed circle: I[8.5; 1.69108846528]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.5555445994° = 169°33'20″ = 0.18222918563 rad
∠ B' = β' = 157.4988320226° = 157°29'54″ = 0.39327283993 rad
∠ C' = γ' = 32.94662337803° = 32°56'46″ = 2.5676572398 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 = 9 ; ; b = 19 ; ; c = 27 ; ;

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

p = a+b+c = 9+19+27 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-9)(27.5-19)(27.5-27) } ; ; T = sqrt{ 2162.19 } = 46.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 46.5 }{ 9 } = 10.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 46.5 }{ 19 } = 4.89 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 46.5 }{ 27 } = 3.44 ; ;

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{ 9**2-19**2-27**2 }{ 2 * 19 * 27 } ) = 10° 26'40" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-9**2-27**2 }{ 2 * 9 * 27 } ) = 22° 30'6" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-9**2-19**2 }{ 2 * 19 * 9 } ) = 147° 3'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 46.5 }{ 27.5 } = 1.69 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 10° 26'40" } = 24.82 ; ;




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