12 24 29 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 24   c = 29

Area: T = 140.7876851304
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 23.86435522517° = 23°51'49″ = 0.4166497558 rad
Angle ∠ B = β = 54.0110025852° = 54°36″ = 0.94326527802 rad
Angle ∠ C = γ = 102.1266421896° = 102°7'35″ = 1.78224423154 rad

Height: ha = 23.46444752173
Height: hb = 11.73222376086
Height: hc = 9.70994380209

Median: ma = 25.93326049598
Median: mb = 18.66881547026
Median: mc = 12.23772382505

Inradius: r = 4.3321903117
Circumradius: R = 14.83109304503

Vertex coordinates: A[29; 0] B[0; 0] C[7.05217241379; 9.70994380209]
Centroid: CG[12.01772413793; 3.23664793403]
Coordinates of the circumscribed circle: U[14.5; -3.11655253203]
Coordinates of the inscribed circle: I[8.5; 4.3321903117]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.1366447748° = 156°8'11″ = 0.4166497558 rad
∠ B' = β' = 125.9989974148° = 125°59'24″ = 0.94326527802 rad
∠ C' = γ' = 77.87435781037° = 77°52'25″ = 1.78224423154 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 = 12 ; ; b = 24 ; ; c = 29 ; ;

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

p = a+b+c = 12+24+29 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-12)(32.5-24)(32.5-29) } ; ; T = sqrt{ 19820.94 } = 140.79 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 140.79 }{ 12 } = 23.46 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 140.79 }{ 24 } = 11.73 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 140.79 }{ 29 } = 9.71 ; ;

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{ 12**2-24**2-29**2 }{ 2 * 24 * 29 } ) = 23° 51'49" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-12**2-29**2 }{ 2 * 12 * 29 } ) = 54° 36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-12**2-24**2 }{ 2 * 24 * 12 } ) = 102° 7'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 140.79 }{ 32.5 } = 4.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 23° 51'49" } = 14.83 ; ;




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