8 24 29 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 24   c = 29

Area: T = 81.79881509571
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 13.59546973238° = 13°35'41″ = 0.23772722291 rad
Angle ∠ B = β = 44.84221867146° = 44°50'32″ = 0.7832643802 rad
Angle ∠ C = γ = 121.5633115962° = 121°33'47″ = 2.12216766225 rad

Height: ha = 20.45495377393
Height: hb = 6.81765125798
Height: hc = 5.64112517901

Median: ma = 26.31553947339
Median: mb = 17.56441680703
Median: mc = 10.47661634199

Inradius: r = 2.68219065888
Circumradius: R = 17.01774995854

Vertex coordinates: A[29; 0] B[0; 0] C[5.67224137931; 5.64112517901]
Centroid: CG[11.55774712644; 1.88804172634]
Coordinates of the circumscribed circle: U[14.5; -8.90875974392]
Coordinates of the inscribed circle: I[6.5; 2.68219065888]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.4055302676° = 166°24'19″ = 0.23772722291 rad
∠ B' = β' = 135.1587813285° = 135°9'28″ = 0.7832643802 rad
∠ C' = γ' = 58.43768840384° = 58°26'13″ = 2.12216766225 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 = 24 ; ; c = 29 ; ;

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

p = a+b+c = 8+24+29 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-8)(30.5-24)(30.5-29) } ; ; T = sqrt{ 6690.94 } = 81.8 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 81.8 }{ 8 } = 20.45 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 81.8 }{ 24 } = 6.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 81.8 }{ 29 } = 5.64 ; ;

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**2-24**2-29**2 }{ 2 * 24 * 29 } ) = 13° 35'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-8**2-29**2 }{ 2 * 8 * 29 } ) = 44° 50'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-8**2-24**2 }{ 2 * 24 * 8 } ) = 121° 33'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 81.8 }{ 30.5 } = 2.68 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 13° 35'41" } = 17.02 ; ;




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