3 11 13 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 11   c = 13

Area: T = 13.3111179512
Perimeter: p = 27
Semiperimeter: s = 13.5

Angle ∠ A = α = 10.72993735799° = 10°43'46″ = 0.18772628956 rad
Angle ∠ B = β = 43.04990798002° = 43°2'57″ = 0.75113481825 rad
Angle ∠ C = γ = 126.222154662° = 126°13'18″ = 2.20329815755 rad

Height: ha = 8.87441196746
Height: hb = 2.42202144567
Height: hc = 2.04878737711

Median: ma = 11.94878031453
Median: mb = 7.66548548584
Median: mc = 4.77696960071

Inradius: r = 0.98660132972
Circumradius: R = 8.05771372284

Vertex coordinates: A[13; 0] B[0; 0] C[2.19223076923; 2.04878737711]
Centroid: CG[5.06441025641; 0.68326245904]
Coordinates of the circumscribed circle: U[6.5; -4.7611035635]
Coordinates of the inscribed circle: I[2.5; 0.98660132972]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.271062642° = 169°16'14″ = 0.18772628956 rad
∠ B' = β' = 136.95109202° = 136°57'3″ = 0.75113481825 rad
∠ C' = γ' = 53.77884533802° = 53°46'42″ = 2.20329815755 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 = 3 ; ; b = 11 ; ; c = 13 ; ;

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

p = a+b+c = 3+11+13 = 27 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 27 }{ 2 } = 13.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.5 * (13.5-3)(13.5-11)(13.5-13) } ; ; T = sqrt{ 177.19 } = 13.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 13.31 }{ 3 } = 8.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 13.31 }{ 11 } = 2.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 13.31 }{ 13 } = 2.05 ; ;

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{ 3**2-11**2-13**2 }{ 2 * 11 * 13 } ) = 10° 43'46" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-3**2-13**2 }{ 2 * 3 * 13 } ) = 43° 2'57" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 13**2-3**2-11**2 }{ 2 * 11 * 3 } ) = 126° 13'18" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 13.31 }{ 13.5 } = 0.99 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 10° 43'46" } = 8.06 ; ;




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