9 23 29 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 23   c = 29

Area: T = 85.89105553597
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 14.92443160109° = 14°55'28″ = 0.2660478453 rad
Angle ∠ B = β = 41.16600882965° = 41°9'36″ = 0.71883790612 rad
Angle ∠ C = γ = 123.9165595693° = 123°54'56″ = 2.16327351394 rad

Height: ha = 19.08767900799
Height: hb = 7.46987439443
Height: hc = 5.92334865765

Median: ma = 25.78327461687
Median: mb = 18.13114643645
Median: mc = 9.7343961167

Inradius: r = 2.81660837823
Circumradius: R = 17.47328175143

Vertex coordinates: A[29; 0] B[0; 0] C[6.7765862069; 5.92334865765]
Centroid: CG[11.92552873563; 1.97444955255]
Coordinates of the circumscribed circle: U[14.5; -9.74993257145]
Coordinates of the inscribed circle: I[7.5; 2.81660837823]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.0765683989° = 165°4'32″ = 0.2660478453 rad
∠ B' = β' = 138.8439911704° = 138°50'24″ = 0.71883790612 rad
∠ C' = γ' = 56.08444043074° = 56°5'4″ = 2.16327351394 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 = 9 ; ; b = 23 ; ; c = 29 ; ;

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

p = a+b+c = 9+23+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 * (30.5-9)(30.5-23)(30.5-29) } ; ; T = sqrt{ 7377.19 } = 85.89 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 85.89 }{ 9 } = 19.09 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 85.89 }{ 23 } = 7.47 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 85.89 }{ 29 } = 5.92 ; ;

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{ 9**2-23**2-29**2 }{ 2 * 23 * 29 } ) = 14° 55'28" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-9**2-29**2 }{ 2 * 9 * 29 } ) = 41° 9'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-9**2-23**2 }{ 2 * 23 * 9 } ) = 123° 54'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 85.89 }{ 30.5 } = 2.82 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 14° 55'28" } = 17.47 ; ;




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