2 27 27 triangle

Acute isosceles triangle.

Sides: a = 2   b = 27   c = 27

Area: T = 26.98114751265
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 4.24551027243° = 4°14'42″ = 0.07440910196 rad
Angle ∠ B = β = 87.87774486379° = 87°52'39″ = 1.5343750817 rad
Angle ∠ C = γ = 87.87774486379° = 87°52'39″ = 1.5343750817 rad

Height: ha = 26.98114751265
Height: hb = 1.99986277871
Height: hc = 1.99986277871

Median: ma = 26.98114751265
Median: mb = 13.57438719605
Median: mc = 13.57438719605

Inradius: r = 0.96436241117
Circumradius: R = 13.50992687961

Vertex coordinates: A[27; 0] B[0; 0] C[0.07440740741; 1.99986277871]
Centroid: CG[9.0254691358; 0.66662092624]
Coordinates of the circumscribed circle: U[13.5; 0.55003432887]
Coordinates of the inscribed circle: I[1; 0.96436241117]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 175.7554897276° = 175°45'18″ = 0.07440910196 rad
∠ B' = β' = 92.12325513621° = 92°7'21″ = 1.5343750817 rad
∠ C' = γ' = 92.12325513621° = 92°7'21″ = 1.5343750817 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 = 2 ; ; b = 27 ; ; c = 27 ; ;

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

p = a+b+c = 2+27+27 = 56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56 }{ 2 } = 28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28 * (28-2)(28-27)(28-27) } ; ; T = sqrt{ 728 } = 26.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 26.98 }{ 2 } = 26.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 26.98 }{ 27 } = 2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 26.98 }{ 27 } = 2 ; ;

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{ 2**2-27**2-27**2 }{ 2 * 27 * 27 } ) = 4° 14'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-2**2-27**2 }{ 2 * 2 * 27 } ) = 87° 52'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-2**2-27**2 }{ 2 * 27 * 2 } ) = 87° 52'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 26.98 }{ 28 } = 0.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 4° 14'42" } = 13.51 ; ;




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