6 27 29 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 27   c = 29

Area: T = 78.74400787401
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 11.60327000765° = 11°36'10″ = 0.20325053185 rad
Angle ∠ B = β = 64.83111465158° = 64°49'52″ = 1.13215169645 rad
Angle ∠ C = γ = 103.5666153408° = 103°33'58″ = 1.80875703706 rad

Height: ha = 26.24766929134
Height: hb = 5.83325984252
Height: hc = 5.43303502579

Median: ma = 27.85767765544
Median: mb = 16.00878105936
Median: mc = 13.12444047484

Inradius: r = 2.544000254
Circumradius: R = 14.91661649162

Vertex coordinates: A[29; 0] B[0; 0] C[2.55217241379; 5.43303502579]
Centroid: CG[10.51772413793; 1.81101167526]
Coordinates of the circumscribed circle: U[14.5; -3.49988534989]
Coordinates of the inscribed circle: I[4; 2.544000254]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.3977299923° = 168°23'50″ = 0.20325053185 rad
∠ B' = β' = 115.1698853484° = 115°10'8″ = 1.13215169645 rad
∠ C' = γ' = 76.43438465923° = 76°26'2″ = 1.80875703706 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 = 6 ; ; b = 27 ; ; c = 29 ; ;

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

p = a+b+c = 6+27+29 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-6)(31-27)(31-29) } ; ; T = sqrt{ 6200 } = 78.74 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 78.74 }{ 6 } = 26.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 78.74 }{ 27 } = 5.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 78.74 }{ 29 } = 5.43 ; ;

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{ 6**2-27**2-29**2 }{ 2 * 27 * 29 } ) = 11° 36'10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-6**2-29**2 }{ 2 * 6 * 29 } ) = 64° 49'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-6**2-27**2 }{ 2 * 27 * 6 } ) = 103° 33'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 78.74 }{ 31 } = 2.54 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 11° 36'10" } = 14.92 ; ;




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