13 22 29 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 22   c = 29

Area: T = 135.0565544129
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 25.04876351928° = 25°2'52″ = 0.4377163704 rad
Angle ∠ B = β = 45.7644214424° = 45°45'51″ = 0.79987362213 rad
Angle ∠ C = γ = 109.1888150383° = 109°11'17″ = 1.90656927284 rad

Height: ha = 20.77877760199
Height: hb = 12.2787776739
Height: hc = 9.31441754572

Median: ma = 24.90548188108
Median: mb = 19.59659179423
Median: mc = 10.78219293264

Inradius: r = 4.2220485754
Circumradius: R = 15.35329424754

Vertex coordinates: A[29; 0] B[0; 0] C[9.06989655172; 9.31441754572]
Centroid: CG[12.69896551724; 3.10547251524]
Coordinates of the circumscribed circle: U[14.5; -5.04660720024]
Coordinates of the inscribed circle: I[10; 4.2220485754]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.9522364807° = 154°57'8″ = 0.4377163704 rad
∠ B' = β' = 134.2365785576° = 134°14'9″ = 0.79987362213 rad
∠ C' = γ' = 70.81218496167° = 70°48'43″ = 1.90656927284 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 = 13 ; ; b = 22 ; ; c = 29 ; ;

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

p = a+b+c = 13+22+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 * (32-13)(32-22)(32-29) } ; ; T = sqrt{ 18240 } = 135.06 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 135.06 }{ 13 } = 20.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 135.06 }{ 22 } = 12.28 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 135.06 }{ 29 } = 9.31 ; ;

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{ 13**2-22**2-29**2 }{ 2 * 22 * 29 } ) = 25° 2'52" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-13**2-29**2 }{ 2 * 13 * 29 } ) = 45° 45'51" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-13**2-22**2 }{ 2 * 22 * 13 } ) = 109° 11'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 135.06 }{ 32 } = 4.22 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 25° 2'52" } = 15.35 ; ;




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