8 26 30 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 26   c = 30

Area: T = 96
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 14.25500326978° = 14°15' = 0.24987099891 rad
Angle ∠ B = β = 53.13301023542° = 53°7'48″ = 0.9277295218 rad
Angle ∠ C = γ = 112.6219864948° = 112°37'11″ = 1.96655874465 rad

Height: ha = 24
Height: hb = 7.38546153846
Height: hc = 6.4

Median: ma = 27.78548879789
Median: mb = 17.6921806013
Median: mc = 12.04215945788

Inradius: r = 3
Circumradius: R = 16.25

Vertex coordinates: A[30; 0] B[0; 0] C[4.8; 6.4]
Centroid: CG[11.6; 2.13333333333]
Coordinates of the circumscribed circle: U[15; -6.25]
Coordinates of the inscribed circle: I[6; 3]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.7549967302° = 165°45' = 0.24987099891 rad
∠ B' = β' = 126.8769897646° = 126°52'12″ = 0.9277295218 rad
∠ C' = γ' = 67.3880135052° = 67°22'49″ = 1.96655874465 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 = 26 ; ; c = 30 ; ;

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

p = a+b+c = 8+26+30 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-8)(32-26)(32-30) } ; ; T = sqrt{ 9216 } = 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 * 96 }{ 8 } = 24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 96 }{ 26 } = 7.38 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 96 }{ 30 } = 6.4 ; ;

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**2-26**2-30**2 }{ 2 * 26 * 30 } ) = 14° 15' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-8**2-30**2 }{ 2 * 8 * 30 } ) = 53° 7'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-8**2-26**2 }{ 2 * 26 * 8 } ) = 112° 37'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 96 }{ 32 } = 3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 14° 15' } = 16.25 ; ;




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