3 28 28 triangle

Acute isosceles triangle.

Sides: a = 3   b = 28   c = 28

Area: T = 41.943968884
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 6.14217736222° = 6°8'30″ = 0.10771941716 rad
Angle ∠ B = β = 86.92991131889° = 86°55'45″ = 1.5177199241 rad
Angle ∠ C = γ = 86.92991131889° = 86°55'45″ = 1.5177199241 rad

Height: ha = 27.965979256
Height: hb = 2.996569206
Height: hc = 2.996569206

Median: ma = 27.965979256
Median: mb = 14.16598022585
Median: mc = 14.16598022585

Inradius: r = 1.42216843675
Circumradius: R = 14.022013263

Vertex coordinates: A[28; 0] B[0; 0] C[0.16107142857; 2.996569206]
Centroid: CG[9.38769047619; 0.999856402]
Coordinates of the circumscribed circle: U[14; 0.75110785338]
Coordinates of the inscribed circle: I[1.5; 1.42216843675]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.8588226378° = 173°51'30″ = 0.10771941716 rad
∠ B' = β' = 93.07108868111° = 93°4'15″ = 1.5177199241 rad
∠ C' = γ' = 93.07108868111° = 93°4'15″ = 1.5177199241 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 = 3 ; ; b = 28 ; ; c = 28 ; ;

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

p = a+b+c = 3+28+28 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-3)(29.5-28)(29.5-28) } ; ; T = sqrt{ 1758.94 } = 41.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 41.94 }{ 3 } = 27.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 41.94 }{ 28 } = 3 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 41.94 }{ 28 } = 3 ; ;

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{ 3**2-28**2-28**2 }{ 2 * 28 * 28 } ) = 6° 8'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-3**2-28**2 }{ 2 * 3 * 28 } ) = 86° 55'45" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-3**2-28**2 }{ 2 * 28 * 3 } ) = 86° 55'45" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 41.94 }{ 29.5 } = 1.42 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 6° 8'30" } = 14.02 ; ;




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