8 22 29 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 22   c = 29

Area: T = 48.76992269777
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 8.79439559871° = 8°47'38″ = 0.15334834863 rad
Angle ∠ B = β = 24.86113826687° = 24°51'41″ = 0.43439129842 rad
Angle ∠ C = γ = 146.3454661344° = 146°20'41″ = 2.55441961832 rad

Height: ha = 12.19223067444
Height: hb = 4.43435660889
Height: hc = 3.3633394964

Median: ma = 25.42663642702
Median: mb = 18.2077141456
Median: mc = 7.98443597113

Inradius: r = 1.65331941348
Circumradius: R = 26.1644039889

Vertex coordinates: A[29; 0] B[0; 0] C[7.25986206897; 3.3633394964]
Centroid: CG[12.08662068966; 1.12111316547]
Coordinates of the circumscribed circle: U[14.5; -21.77985900212]
Coordinates of the inscribed circle: I[7.5; 1.65331941348]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.2066044013° = 171°12'22″ = 0.15334834863 rad
∠ B' = β' = 155.1398617331° = 155°8'19″ = 0.43439129842 rad
∠ C' = γ' = 33.65553386559° = 33°39'19″ = 2.55441961832 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 = 22 ; ; c = 29 ; ;

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

p = a+b+c = 8+22+29 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-8)(29.5-22)(29.5-29) } ; ; T = sqrt{ 2378.44 } = 48.77 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 48.77 }{ 8 } = 12.19 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 48.77 }{ 22 } = 4.43 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 48.77 }{ 29 } = 3.36 ; ;

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**2-22**2-29**2 }{ 2 * 22 * 29 } ) = 8° 47'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-8**2-29**2 }{ 2 * 8 * 29 } ) = 24° 51'41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-8**2-22**2 }{ 2 * 22 * 8 } ) = 146° 20'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 48.77 }{ 29.5 } = 1.65 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 8° 47'38" } = 26.16 ; ;




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