6 28 28 triangle

Acute isosceles triangle.

Sides: a = 6   b = 28   c = 28

Area: T = 83.51664654425
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 12.30112796559° = 12°18'5″ = 0.21546978322 rad
Angle ∠ B = β = 83.84993601721° = 83°50'58″ = 1.46334474107 rad
Angle ∠ C = γ = 83.84993601721° = 83°50'58″ = 1.46334474107 rad

Height: ha = 27.83988218142
Height: hb = 5.96554618173
Height: hc = 5.96554618173

Median: ma = 27.83988218142
Median: mb = 14.62987388383
Median: mc = 14.62987388383

Inradius: r = 2.69440795304
Circumradius: R = 14.08110556789

Vertex coordinates: A[28; 0] B[0; 0] C[0.64328571429; 5.96554618173]
Centroid: CG[9.54876190476; 1.98884872724]
Coordinates of the circumscribed circle: U[14; 1.5098684537]
Coordinates of the inscribed circle: I[3; 2.69440795304]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.6998720344° = 167°41'55″ = 0.21546978322 rad
∠ B' = β' = 96.15106398279° = 96°9'2″ = 1.46334474107 rad
∠ C' = γ' = 96.15106398279° = 96°9'2″ = 1.46334474107 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 = 6 ; ; b = 28 ; ; c = 28 ; ;

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

p = a+b+c = 6+28+28 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-6)(31-28)(31-28) } ; ; T = sqrt{ 6975 } = 83.52 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 83.52 }{ 6 } = 27.84 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 83.52 }{ 28 } = 5.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 83.52 }{ 28 } = 5.97 ; ;

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{ 6**2-28**2-28**2 }{ 2 * 28 * 28 } ) = 12° 18'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-6**2-28**2 }{ 2 * 6 * 28 } ) = 83° 50'58" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-6**2-28**2 }{ 2 * 28 * 6 } ) = 83° 50'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 83.52 }{ 31 } = 2.69 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 12° 18'5" } = 14.08 ; ;




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