8 16 23 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 16   c = 23

Area: T = 36.95985916939
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 11.58773657813° = 11°35'15″ = 0.20222376845 rad
Angle ∠ B = β = 23.68659872791° = 23°41'10″ = 0.41333984646 rad
Angle ∠ C = γ = 144.727664694° = 144°43'36″ = 2.52659565045 rad

Height: ha = 9.24396479235
Height: hb = 4.62198239617
Height: hc = 3.21437905821

Median: ma = 19.40436079119
Median: mb = 15.2487950682
Median: mc = 5.26878268764

Inradius: r = 1.57327060295
Circumradius: R = 19.91441787137

Vertex coordinates: A[23; 0] B[0; 0] C[7.32660869565; 3.21437905821]
Centroid: CG[10.10986956522; 1.07112635274]
Coordinates of the circumscribed circle: U[11.5; -16.25880599655]
Coordinates of the inscribed circle: I[7.5; 1.57327060295]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.4132634219° = 168°24'45″ = 0.20222376845 rad
∠ B' = β' = 156.3144012721° = 156°18'50″ = 0.41333984646 rad
∠ C' = γ' = 35.27333530604° = 35°16'24″ = 2.52659565045 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 = 16 ; ; c = 23 ; ;

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

p = a+b+c = 8+16+23 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-8)(23.5-16)(23.5-23) } ; ; T = sqrt{ 1365.94 } = 36.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 36.96 }{ 8 } = 9.24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 36.96 }{ 16 } = 4.62 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 36.96 }{ 23 } = 3.21 ; ;

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**2-16**2-23**2 }{ 2 * 16 * 23 } ) = 11° 35'15" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-8**2-23**2 }{ 2 * 8 * 23 } ) = 23° 41'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-8**2-16**2 }{ 2 * 16 * 8 } ) = 144° 43'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 36.96 }{ 23.5 } = 1.57 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 11° 35'15" } = 19.91 ; ;




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