11 11 13 triangle

Acute isosceles triangle.

Sides: a = 11   b = 11   c = 13

Area: T = 57.68217778852
Perimeter: p = 35
Semiperimeter: s = 17.5

Angle ∠ A = α = 53.77884533802° = 53°46'42″ = 0.93986110781 rad
Angle ∠ B = β = 53.77884533802° = 53°46'42″ = 0.93986110781 rad
Angle ∠ C = γ = 72.44330932397° = 72°26'35″ = 1.26443704974 rad

Height: ha = 10.48875959791
Height: hb = 10.48875959791
Height: hc = 8.87441196746

Median: ma = 10.71221426428
Median: mb = 10.71221426428
Median: mc = 8.87441196746

Inradius: r = 3.29661015934
Circumradius: R = 6.81875776548

Vertex coordinates: A[13; 0] B[0; 0] C[6.5; 8.87441196746]
Centroid: CG[6.5; 2.95880398915]
Coordinates of the circumscribed circle: U[6.5; 2.05765420198]
Coordinates of the inscribed circle: I[6.5; 3.29661015934]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.222154662° = 126°13'18″ = 0.93986110781 rad
∠ B' = β' = 126.222154662° = 126°13'18″ = 0.93986110781 rad
∠ C' = γ' = 107.557690676° = 107°33'25″ = 1.26443704974 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 = 11 ; ; b = 11 ; ; c = 13 ; ;

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

p = a+b+c = 11+11+13 = 35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 35 }{ 2 } = 17.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.5 * (17.5-11)(17.5-11)(17.5-13) } ; ; T = sqrt{ 3327.19 } = 57.68 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 57.68 }{ 11 } = 10.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 57.68 }{ 11 } = 10.49 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 57.68 }{ 13 } = 8.87 ; ;

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{ 11**2-11**2-13**2 }{ 2 * 11 * 13 } ) = 53° 46'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-11**2-13**2 }{ 2 * 11 * 13 } ) = 53° 46'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 13**2-11**2-11**2 }{ 2 * 11 * 11 } ) = 72° 26'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 57.68 }{ 17.5 } = 3.3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 53° 46'42" } = 6.82 ; ;




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