11 13 13 triangle

Acute isosceles triangle.

Sides: a = 11   b = 13   c = 13

Area: T = 64.78657044416
Perimeter: p = 37
Semiperimeter: s = 18.5

Angle ∠ A = α = 50.05879989752° = 50°3'29″ = 0.87436768991 rad
Angle ∠ B = β = 64.97110005124° = 64°58'16″ = 1.13439578773 rad
Angle ∠ C = γ = 64.97110005124° = 64°58'16″ = 1.13439578773 rad

Height: ha = 11.77992189894
Height: hb = 9.96770314526
Height: hc = 9.96770314526

Median: ma = 11.77992189894
Median: mb = 10.13765674664
Median: mc = 10.13765674664

Inradius: r = 3.50219299698
Circumradius: R = 7.17436504836

Vertex coordinates: A[13; 0] B[0; 0] C[4.65438461538; 9.96770314526]
Centroid: CG[5.88546153846; 3.32223438175]
Coordinates of the circumscribed circle: U[6.5; 3.03550059738]
Coordinates of the inscribed circle: I[5.5; 3.50219299698]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 129.9422001025° = 129°56'31″ = 0.87436768991 rad
∠ B' = β' = 115.0298999488° = 115°1'44″ = 1.13439578773 rad
∠ C' = γ' = 115.0298999488° = 115°1'44″ = 1.13439578773 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 = 13 ; ; c = 13 ; ;

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

p = a+b+c = 11+13+13 = 37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 37 }{ 2 } = 18.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.5 * (18.5-11)(18.5-13)(18.5-13) } ; ; T = sqrt{ 4197.19 } = 64.79 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 64.79 }{ 11 } = 11.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 64.79 }{ 13 } = 9.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 64.79 }{ 13 } = 9.97 ; ;

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{ 11**2-13**2-13**2 }{ 2 * 13 * 13 } ) = 50° 3'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-11**2-13**2 }{ 2 * 11 * 13 } ) = 64° 58'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 13**2-11**2-13**2 }{ 2 * 13 * 11 } ) = 64° 58'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 64.79 }{ 18.5 } = 3.5 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 50° 3'29" } = 7.17 ; ;




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