9 27 29 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 27   c = 29

Area: T = 121.2532577292
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 18.04219258202° = 18°2'31″ = 0.3154891009 rad
Angle ∠ B = β = 68.30109223033° = 68°18'3″ = 1.19220759763 rad
Angle ∠ C = γ = 93.65771518766° = 93°39'26″ = 1.63546256683 rad

Height: ha = 26.9455017176
Height: hb = 8.9821672392
Height: hc = 8.36222467098

Median: ma = 27.6544113618
Median: mb = 16.69658078571
Median: mc = 13.9555285737

Inradius: r = 3.73108485321
Circumradius: R = 14.5329588066

Vertex coordinates: A[29; 0] B[0; 0] C[3.32875862069; 8.36222467098]
Centroid: CG[10.7765862069; 2.78774155699]
Coordinates of the circumscribed circle: U[14.5; -0.9276784424]
Coordinates of the inscribed circle: I[5.5; 3.73108485321]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.958807418° = 161°57'29″ = 0.3154891009 rad
∠ B' = β' = 111.6999077697° = 111°41'57″ = 1.19220759763 rad
∠ C' = γ' = 86.34328481234° = 86°20'34″ = 1.63546256683 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 = 27 ; ; c = 29 ; ;

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

p = a+b+c = 9+27+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 * (32.5-9)(32.5-27)(32.5-29) } ; ; T = sqrt{ 14702.19 } = 121.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 121.25 }{ 9 } = 26.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 121.25 }{ 27 } = 8.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 121.25 }{ 29 } = 8.36 ; ;

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**2-27**2-29**2 }{ 2 * 27 * 29 } ) = 18° 2'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-9**2-29**2 }{ 2 * 9 * 29 } ) = 68° 18'3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-9**2-27**2 }{ 2 * 27 * 9 } ) = 93° 39'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 121.25 }{ 32.5 } = 3.73 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 18° 2'31" } = 14.53 ; ;




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