28 29 29 triangle

Acute isosceles triangle.

Sides: a = 28   b = 29   c = 29

Area: T = 355.5565902778
Perimeter: p = 86
Semiperimeter: s = 43

Angle ∠ A = α = 57.731145483° = 57°43'53″ = 1.00876039688 rad
Angle ∠ B = β = 61.1344272585° = 61°8'3″ = 1.06769943424 rad
Angle ∠ C = γ = 61.1344272585° = 61°8'3″ = 1.06769943424 rad

Height: ha = 25.39768501984
Height: hb = 24.52110967433
Height: hc = 24.52110967433

Median: ma = 25.39768501984
Median: mb = 24.54107823836
Median: mc = 24.54107823836

Inradius: r = 8.26987419251
Circumradius: R = 16.55771713309

Vertex coordinates: A[29; 0] B[0; 0] C[13.51772413793; 24.52110967433]
Centroid: CG[14.17224137931; 8.17436989144]
Coordinates of the circumscribed circle: U[14.5; 7.99331171942]
Coordinates of the inscribed circle: I[14; 8.26987419251]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 122.269854517° = 122°16'7″ = 1.00876039688 rad
∠ B' = β' = 118.8665727415° = 118°51'57″ = 1.06769943424 rad
∠ C' = γ' = 118.8665727415° = 118°51'57″ = 1.06769943424 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 = 28 ; ; b = 29 ; ; c = 29 ; ;

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

p = a+b+c = 28+29+29 = 86 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 86 }{ 2 } = 43 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 43 * (43-28)(43-29)(43-29) } ; ; T = sqrt{ 126420 } = 355.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 355.56 }{ 28 } = 25.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 355.56 }{ 29 } = 24.52 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 355.56 }{ 29 } = 24.52 ; ;

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{ 28**2-29**2-29**2 }{ 2 * 29 * 29 } ) = 57° 43'53" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-28**2-29**2 }{ 2 * 28 * 29 } ) = 61° 8'3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-28**2-29**2 }{ 2 * 29 * 28 } ) = 61° 8'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 355.56 }{ 43 } = 8.27 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 28 }{ 2 * sin 57° 43'53" } = 16.56 ; ;




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