12 23 29 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 23   c = 29

Area: T = 131.4533413801
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 23.21437927007° = 23°12'50″ = 0.40551571145 rad
Angle ∠ B = β = 49.06772754258° = 49°4'2″ = 0.85663855112 rad
Angle ∠ C = γ = 107.7198931873° = 107°43'8″ = 1.88800500279 rad

Height: ha = 21.90989023002
Height: hb = 11.43107316349
Height: hc = 9.06657526759

Median: ma = 25.47554784057
Median: mb = 18.98802528961
Median: mc = 11.23661025271

Inradius: r = 4.10879191813
Circumradius: R = 15.2222122744

Vertex coordinates: A[29; 0] B[0; 0] C[7.86220689655; 9.06657526759]
Centroid: CG[12.28773563218; 3.02219175586]
Coordinates of the circumscribed circle: U[14.5; -4.63328199656]
Coordinates of the inscribed circle: I[9; 4.10879191813]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.7866207299° = 156°47'10″ = 0.40551571145 rad
∠ B' = β' = 130.9332724574° = 130°55'58″ = 0.85663855112 rad
∠ C' = γ' = 72.28110681266° = 72°16'52″ = 1.88800500279 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 = 23 ; ; c = 29 ; ;

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

p = a+b+c = 12+23+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 * (32-12)(32-23)(32-29) } ; ; T = sqrt{ 17280 } = 131.45 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 131.45 }{ 12 } = 21.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 131.45 }{ 23 } = 11.43 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 131.45 }{ 29 } = 9.07 ; ;

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**2-23**2-29**2 }{ 2 * 23 * 29 } ) = 23° 12'50" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-12**2-29**2 }{ 2 * 12 * 29 } ) = 49° 4'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-12**2-23**2 }{ 2 * 23 * 12 } ) = 107° 43'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 131.45 }{ 32 } = 4.11 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 23° 12'50" } = 15.22 ; ;




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