5 26 29 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 26   c = 29

Area: T = 54.77222557505
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 8.35437541814° = 8°21'14″ = 0.14658005154 rad
Angle ∠ B = β = 49.06772754258° = 49°4'2″ = 0.85663855112 rad
Angle ∠ C = γ = 122.5798970393° = 122°34'44″ = 2.13994066271 rad

Height: ha = 21.90989023002
Height: hb = 4.21332504423
Height: hc = 3.77773969483

Median: ma = 27.42771763038
Median: mb = 16.24880768093
Median: mc = 11.84327192823

Inradius: r = 1.82657418584
Circumradius: R = 17.2087617015

Vertex coordinates: A[29; 0] B[0; 0] C[3.2765862069; 3.77773969483]
Centroid: CG[10.75986206897; 1.25991323161]
Coordinates of the circumscribed circle: U[14.5; -9.26656399311]
Coordinates of the inscribed circle: I[4; 1.82657418584]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.6466245819° = 171°38'47″ = 0.14658005154 rad
∠ B' = β' = 130.9332724574° = 130°55'58″ = 0.85663855112 rad
∠ C' = γ' = 57.42110296072° = 57°25'16″ = 2.13994066271 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 = 5 ; ; b = 26 ; ; c = 29 ; ;

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

p = a+b+c = 5+26+29 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-5)(30-26)(30-29) } ; ; T = sqrt{ 3000 } = 54.77 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 54.77 }{ 5 } = 21.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 54.77 }{ 26 } = 4.21 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 54.77 }{ 29 } = 3.78 ; ;

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{ 5**2-26**2-29**2 }{ 2 * 26 * 29 } ) = 8° 21'14" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-5**2-29**2 }{ 2 * 5 * 29 } ) = 49° 4'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-5**2-26**2 }{ 2 * 26 * 5 } ) = 122° 34'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 54.77 }{ 30 } = 1.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 8° 21'14" } = 17.21 ; ;




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