26 28 29 triangle

Acute scalene triangle.

Sides: a = 26   b = 28   c = 29

Area: T = 329.4676898944
Perimeter: p = 83
Semiperimeter: s = 41.5

Angle ∠ A = α = 54.24222380202° = 54°14'32″ = 0.94767056471 rad
Angle ∠ B = β = 60.9177120308° = 60°55'2″ = 1.06332043202 rad
Angle ∠ C = γ = 64.84106416718° = 64°50'26″ = 1.13216826863 rad

Height: ha = 25.34436076111
Height: hb = 23.53333499246
Height: hc = 22.72218550996

Median: ma = 25.36773017879
Median: mb = 23.71770824513
Median: mc = 22.79880262304

Inradius: r = 7.93989614203
Circumradius: R = 16.02198187342

Vertex coordinates: A[29; 0] B[0; 0] C[12.63879310345; 22.72218550996]
Centroid: CG[13.87993103448; 7.57439516999]
Coordinates of the circumscribed circle: U[14.5; 6.81106234866]
Coordinates of the inscribed circle: I[13.5; 7.93989614203]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.758776198° = 125°45'28″ = 0.94767056471 rad
∠ B' = β' = 119.0832879692° = 119°4'58″ = 1.06332043202 rad
∠ C' = γ' = 115.1599358328° = 115°9'34″ = 1.13216826863 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 = 28 ; ; c = 29 ; ;

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

p = a+b+c = 26+28+29 = 83 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 83 }{ 2 } = 41.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 41.5 * (41.5-26)(41.5-28)(41.5-29) } ; ; T = sqrt{ 108548.44 } = 329.47 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 329.47 }{ 26 } = 25.34 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 329.47 }{ 28 } = 23.53 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 329.47 }{ 29 } = 22.72 ; ;

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**2-28**2-29**2 }{ 2 * 28 * 29 } ) = 54° 14'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-26**2-29**2 }{ 2 * 26 * 29 } ) = 60° 55'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-26**2-28**2 }{ 2 * 28 * 26 } ) = 64° 50'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 329.47 }{ 41.5 } = 7.94 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 26 }{ 2 * sin 54° 14'32" } = 16.02 ; ;




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