1 11 11 triangle

Acute isosceles triangle.

Sides: a = 1   b = 11   c = 11

Area: T = 5.4944315244
Perimeter: p = 23
Semiperimeter: s = 11.5

Angle ∠ A = α = 5.21105025301° = 5°12'38″ = 0.09109404248 rad
Angle ∠ B = β = 87.39547487349° = 87°23'41″ = 1.52553261144 rad
Angle ∠ C = γ = 87.39547487349° = 87°23'41″ = 1.52553261144 rad

Height: ha = 10.98986304879
Height: hb = 0.9998966408
Height: hc = 0.9998966408

Median: ma = 10.98986304879
Median: mb = 5.54552682532
Median: mc = 5.54552682532

Inradius: r = 0.4787766543
Circumradius: R = 5.50656906378

Vertex coordinates: A[11; 0] B[0; 0] C[0.04554545455; 0.9998966408]
Centroid: CG[3.68218181818; 0.33329888027]
Coordinates of the circumscribed circle: U[5.5; 0.25502586654]
Coordinates of the inscribed circle: I[0.5; 0.4787766543]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 174.789949747° = 174°47'22″ = 0.09109404248 rad
∠ B' = β' = 92.60552512651° = 92°36'19″ = 1.52553261144 rad
∠ C' = γ' = 92.60552512651° = 92°36'19″ = 1.52553261144 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 = 11 ; ; c = 11 ; ;

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

p = a+b+c = 1+11+11 = 23 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 23 }{ 2 } = 11.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.5 * (11.5-1)(11.5-11)(11.5-11) } ; ; T = sqrt{ 30.19 } = 5.49 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5.49 }{ 1 } = 10.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5.49 }{ 11 } = 1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5.49 }{ 11 } = 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**2-11**2-11**2 }{ 2 * 11 * 11 } ) = 5° 12'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-1**2-11**2 }{ 2 * 1 * 11 } ) = 87° 23'41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11**2-1**2-11**2 }{ 2 * 11 * 1 } ) = 87° 23'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5.49 }{ 11.5 } = 0.48 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1 }{ 2 * sin 5° 12'38" } = 5.51 ; ;




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