9 26 29 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 26   c = 29

Area: T = 115.109995656
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 17.77765098334° = 17°46'35″ = 0.31102586261 rad
Angle ∠ B = β = 61.88435992727° = 61°53'1″ = 1.08800725603 rad
Angle ∠ C = γ = 100.3439890894° = 100°20'24″ = 1.75112614672 rad

Height: ha = 25.57877681243
Height: hb = 8.85438428123
Height: hc = 7.93879280386

Median: ma = 27.17107563384
Median: mb = 17.08880074906
Median: mc = 12.97111217711

Inradius: r = 3.59768736425
Circumradius: R = 14.73993626437

Vertex coordinates: A[29; 0] B[0; 0] C[4.24113793103; 7.93879280386]
Centroid: CG[11.08804597701; 2.64659760129]
Coordinates of the circumscribed circle: U[14.5; -2.64655266283]
Coordinates of the inscribed circle: I[6; 3.59768736425]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.2233490167° = 162°13'25″ = 0.31102586261 rad
∠ B' = β' = 118.1166400727° = 118°6'59″ = 1.08800725603 rad
∠ C' = γ' = 79.66601091061° = 79°39'36″ = 1.75112614672 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 = 26 ; ; c = 29 ; ;

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

p = a+b+c = 9+26+29 = 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 * (32-9)(32-26)(32-29) } ; ; T = sqrt{ 13248 } = 115.1 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 115.1 }{ 9 } = 25.58 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 115.1 }{ 26 } = 8.85 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 115.1 }{ 29 } = 7.94 ; ;

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**2-26**2-29**2 }{ 2 * 26 * 29 } ) = 17° 46'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-9**2-29**2 }{ 2 * 9 * 29 } ) = 61° 53'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-9**2-26**2 }{ 2 * 26 * 9 } ) = 100° 20'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 115.1 }{ 32 } = 3.6 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 17° 46'35" } = 14.74 ; ;




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