1 28 28 triangle

Acute isosceles triangle.

Sides: a = 1   b = 28   c = 28

Area: T = 13.99877676792
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 2.04663866074° = 2°2'47″ = 0.03657161841 rad
Angle ∠ B = β = 88.97768066963° = 88°58'37″ = 1.55329382348 rad
Angle ∠ C = γ = 88.97768066963° = 88°58'37″ = 1.55329382348 rad

Height: ha = 27.99655353583
Height: hb = 10.9998405485
Height: hc = 10.9998405485

Median: ma = 27.99655353583
Median: mb = 14.01878457689
Median: mc = 14.01878457689

Inradius: r = 0.49111497431
Circumradius: R = 14.00222326768

Vertex coordinates: A[28; 0] B[0; 0] C[0.01878571429; 10.9998405485]
Centroid: CG[9.33992857143; 0.33332801828]
Coordinates of the circumscribed circle: U[14; 0.25500398692]
Coordinates of the inscribed circle: I[0.5; 0.49111497431]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 177.9543613393° = 177°57'13″ = 0.03657161841 rad
∠ B' = β' = 91.02331933037° = 91°1'23″ = 1.55329382348 rad
∠ C' = γ' = 91.02331933037° = 91°1'23″ = 1.55329382348 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 = 1 ; ; b = 28 ; ; c = 28 ; ;

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

p = a+b+c = 1+28+28 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-1)(28.5-28)(28.5-28) } ; ; T = sqrt{ 195.94 } = 14 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 14 }{ 1 } = 28 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 14 }{ 28 } = 1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 14 }{ 28 } = 1 ; ;

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{ 1**2-28**2-28**2 }{ 2 * 28 * 28 } ) = 2° 2'47" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-1**2-28**2 }{ 2 * 1 * 28 } ) = 88° 58'37" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-1**2-28**2 }{ 2 * 28 * 1 } ) = 88° 58'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 14 }{ 28.5 } = 0.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1 }{ 2 * sin 2° 2'47" } = 14 ; ;




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