28 28 29 triangle

Acute isosceles triangle.

Sides: a = 28   b = 28   c = 29

Area: T = 347.3219647443
Perimeter: p = 85
Semiperimeter: s = 42.5

Angle ∠ A = α = 58.81113776665° = 58°48'41″ = 1.02664521779 rad
Angle ∠ B = β = 58.81113776665° = 58°48'41″ = 1.02664521779 rad
Angle ∠ C = γ = 62.3777244667° = 62°22'38″ = 1.08986882978 rad

Height: ha = 24.80985462459
Height: hb = 24.80985462459
Height: hc = 23.9533079134

Median: ma = 24.82994180359
Median: mb = 24.82994180359
Median: mc = 23.9533079134

Inradius: r = 8.17222269987
Circumradius: R = 16.36553281404

Vertex coordinates: A[29; 0] B[0; 0] C[14.5; 23.9533079134]
Centroid: CG[14.5; 7.98443597113]
Coordinates of the circumscribed circle: U[14.5; 7.58877509936]
Coordinates of the inscribed circle: I[14.5; 8.17222269987]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 121.1898622333° = 121°11'19″ = 1.02664521779 rad
∠ B' = β' = 121.1898622333° = 121°11'19″ = 1.02664521779 rad
∠ C' = γ' = 117.6232755333° = 117°37'22″ = 1.08986882978 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 = 28 ; ; c = 29 ; ;

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

p = a+b+c = 28+28+29 = 85 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 85 }{ 2 } = 42.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 42.5 * (42.5-28)(42.5-28)(42.5-29) } ; ; T = sqrt{ 120630.94 } = 347.32 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 347.32 }{ 28 } = 24.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 347.32 }{ 28 } = 24.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 347.32 }{ 29 } = 23.95 ; ;

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**2-28**2-29**2 }{ 2 * 28 * 29 } ) = 58° 48'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-28**2-29**2 }{ 2 * 28 * 29 } ) = 58° 48'41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-28**2-28**2 }{ 2 * 28 * 28 } ) = 62° 22'38" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 347.32 }{ 42.5 } = 8.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 28 }{ 2 * sin 58° 48'41" } = 16.37 ; ;




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