8 11 11 triangle

Acute isosceles triangle.

Sides: a = 8   b = 11   c = 11

Area: T = 40.98878030638
Perimeter: p = 30
Semiperimeter: s = 15

Angle ∠ A = α = 42.6477372527° = 42°38'51″ = 0.74443370679 rad
Angle ∠ B = β = 68.67663137365° = 68°40'35″ = 1.19986277928 rad
Angle ∠ C = γ = 68.67663137365° = 68°40'35″ = 1.19986277928 rad

Height: ha = 10.2476950766
Height: hb = 7.45223278298
Height: hc = 7.45223278298

Median: ma = 10.2476950766
Median: mb = 7.8989866919
Median: mc = 7.8989866919

Inradius: r = 2.73325202043
Circumradius: R = 5.90441954413

Vertex coordinates: A[11; 0] B[0; 0] C[2.90990909091; 7.45223278298]
Centroid: CG[4.63663636364; 2.48441092766]
Coordinates of the circumscribed circle: U[5.5; 2.14769801605]
Coordinates of the inscribed circle: I[4; 2.73325202043]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.3532627473° = 137°21'9″ = 0.74443370679 rad
∠ B' = β' = 111.3243686263° = 111°19'25″ = 1.19986277928 rad
∠ C' = γ' = 111.3243686263° = 111°19'25″ = 1.19986277928 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 = 8 ; ; b = 11 ; ; c = 11 ; ;

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

p = a+b+c = 8+11+11 = 30 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 30 }{ 2 } = 15 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15 * (15-8)(15-11)(15-11) } ; ; T = sqrt{ 1680 } = 40.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 40.99 }{ 8 } = 10.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 40.99 }{ 11 } = 7.45 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 40.99 }{ 11 } = 7.45 ; ;

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{ 8**2-11**2-11**2 }{ 2 * 11 * 11 } ) = 42° 38'51" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-8**2-11**2 }{ 2 * 8 * 11 } ) = 68° 40'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11**2-8**2-11**2 }{ 2 * 11 * 8 } ) = 68° 40'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 40.99 }{ 15 } = 2.73 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 42° 38'51" } = 5.9 ; ;




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