8 26 29 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 26   c = 29

Area: T = 100.8888242625
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 15.52219825604° = 15°31'19″ = 0.27109097021 rad
Angle ∠ B = β = 60.42768411792° = 60°25'37″ = 1.05546473352 rad
Angle ∠ C = γ = 104.051117626° = 104°3'4″ = 1.81660356163 rad

Height: ha = 25.22220606563
Height: hb = 7.76106340481
Height: hc = 6.95878098362

Median: ma = 27.24988531869
Median: mb = 16.83774582405
Median: mc = 12.63992246598

Inradius: r = 3.20328013532
Circumradius: R = 14.94772323113

Vertex coordinates: A[29; 0] B[0; 0] C[3.94882758621; 6.95878098362]
Centroid: CG[10.98327586207; 2.31992699454]
Coordinates of the circumscribed circle: U[14.5; -3.62990155371]
Coordinates of the inscribed circle: I[5.5; 3.20328013532]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.478801744° = 164°28'41″ = 0.27109097021 rad
∠ B' = β' = 119.5733158821° = 119°34'23″ = 1.05546473352 rad
∠ C' = γ' = 75.94988237396° = 75°56'56″ = 1.81660356163 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 = 29 ; ;

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

p = a+b+c = 8+26+29 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-8)(31.5-26)(31.5-29) } ; ; T = sqrt{ 10178.44 } = 100.89 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 100.89 }{ 8 } = 25.22 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 100.89 }{ 26 } = 7.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 100.89 }{ 29 } = 6.96 ; ;

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**2-29**2 }{ 2 * 26 * 29 } ) = 15° 31'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-8**2-29**2 }{ 2 * 8 * 29 } ) = 60° 25'37" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-8**2-26**2 }{ 2 * 26 * 8 } ) = 104° 3'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 100.89 }{ 31.5 } = 3.2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 15° 31'19" } = 14.95 ; ;




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