9 22 29 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 22   c = 29

Area: T = 70.99329573972
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 12.85987602998° = 12°51'32″ = 0.2244427705 rad
Angle ∠ B = β = 32.95768545469° = 32°57'25″ = 0.57552056229 rad
Angle ∠ C = γ = 134.1844385153° = 134°11'4″ = 2.34219593257 rad

Height: ha = 15.77662127549
Height: hb = 6.45439052179
Height: hc = 4.89660660274

Median: ma = 25.34326517949
Median: mb = 18.43990889146
Median: mc = 8.5

Inradius: r = 2.36664319132
Circumradius: R = 20.22203155444

Vertex coordinates: A[29; 0] B[0; 0] C[7.55217241379; 4.89660660274]
Centroid: CG[12.1843908046; 1.63220220091]
Coordinates of the circumscribed circle: U[14.5; -14.09329471976]
Coordinates of the inscribed circle: I[8; 2.36664319132]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.14112397° = 167°8'28″ = 0.2244427705 rad
∠ B' = β' = 147.0433145453° = 147°2'35″ = 0.57552056229 rad
∠ C' = γ' = 45.81656148467° = 45°48'56″ = 2.34219593257 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 = 22 ; ; c = 29 ; ;

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

p = a+b+c = 9+22+29 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-9)(30-22)(30-29) } ; ; T = sqrt{ 5040 } = 70.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 70.99 }{ 9 } = 15.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 70.99 }{ 22 } = 6.45 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 70.99 }{ 29 } = 4.9 ; ;

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**2-22**2-29**2 }{ 2 * 22 * 29 } ) = 12° 51'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-9**2-29**2 }{ 2 * 9 * 29 } ) = 32° 57'25" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-9**2-22**2 }{ 2 * 22 * 9 } ) = 134° 11'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 70.99 }{ 30 } = 2.37 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 12° 51'32" } = 20.22 ; ;




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