26 27 29 triangle

Acute scalene triangle.

Sides: a = 26   b = 27   c = 29

Area: T = 321.4344285664
Perimeter: p = 82
Semiperimeter: s = 41

Angle ∠ A = α = 55.1888300788° = 55°11'18″ = 0.96332175573 rad
Angle ∠ B = β = 58.49767842222° = 58°29'48″ = 1.02109614865 rad
Angle ∠ C = γ = 66.31549149898° = 66°18'54″ = 1.15774136098 rad

Height: ha = 24.72657142818
Height: hb = 23.81099470862
Height: hc = 22.16878817699

Median: ma = 24.8199347292
Median: mb = 24.00552077683
Median: mc = 22.18767077323

Inradius: r = 7.84398606259
Circumradius: R = 15.83437185142

Vertex coordinates: A[29; 0] B[0; 0] C[13.58662068966; 22.16878817699]
Centroid: CG[14.19554022989; 7.38992939233]
Coordinates of the circumscribed circle: U[14.5; 6.36105535912]
Coordinates of the inscribed circle: I[14; 7.84398606259]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 124.8121699212° = 124°48'42″ = 0.96332175573 rad
∠ B' = β' = 121.5033215778° = 121°30'12″ = 1.02109614865 rad
∠ C' = γ' = 113.685508501° = 113°41'6″ = 1.15774136098 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 = 26 ; ; b = 27 ; ; c = 29 ; ;

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

p = a+b+c = 26+27+29 = 82 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 82 }{ 2 } = 41 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 41 * (41-26)(41-27)(41-29) } ; ; T = sqrt{ 103320 } = 321.43 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 321.43 }{ 26 } = 24.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 321.43 }{ 27 } = 23.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 321.43 }{ 29 } = 22.17 ; ;

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{ 26**2-27**2-29**2 }{ 2 * 27 * 29 } ) = 55° 11'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-26**2-29**2 }{ 2 * 26 * 29 } ) = 58° 29'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-26**2-27**2 }{ 2 * 27 * 26 } ) = 66° 18'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 321.43 }{ 41 } = 7.84 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 26 }{ 2 * sin 55° 11'18" } = 15.83 ; ;




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