13 13 19 triangle

Obtuse isosceles triangle.

Sides: a = 13   b = 13   c = 19

Area: T = 84.30441369092
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 43.04990798002° = 43°2'57″ = 0.75113481825 rad
Angle ∠ B = β = 43.04990798002° = 43°2'57″ = 0.75113481825 rad
Angle ∠ C = γ = 93.90218403995° = 93°54'7″ = 1.63988962887 rad

Height: ha = 12.97698672168
Height: hb = 12.97698672168
Height: hc = 8.87441196746

Median: ma = 14.92548115566
Median: mb = 14.92548115566
Median: mc = 8.87441196746

Inradius: r = 3.74768505293
Circumradius: R = 9.52220712699

Vertex coordinates: A[19; 0] B[0; 0] C[9.5; 8.87441196746]
Centroid: CG[9.5; 2.95880398915]
Coordinates of the circumscribed circle: U[9.5; -0.64879515953]
Coordinates of the inscribed circle: I[9.5; 3.74768505293]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.95109202° = 136°57'3″ = 0.75113481825 rad
∠ B' = β' = 136.95109202° = 136°57'3″ = 0.75113481825 rad
∠ C' = γ' = 86.09881596005° = 86°5'53″ = 1.63988962887 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 = 13 ; ; b = 13 ; ; c = 19 ; ;

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

p = a+b+c = 13+13+19 = 45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 45 }{ 2 } = 22.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.5 * (22.5-13)(22.5-13)(22.5-19) } ; ; T = sqrt{ 7107.19 } = 84.3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 84.3 }{ 13 } = 12.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 84.3 }{ 13 } = 12.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 84.3 }{ 19 } = 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{ 13**2-13**2-19**2 }{ 2 * 13 * 19 } ) = 43° 2'57" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-13**2-19**2 }{ 2 * 13 * 19 } ) = 43° 2'57" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-13**2-13**2 }{ 2 * 13 * 13 } ) = 93° 54'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 84.3 }{ 22.5 } = 3.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 43° 2'57" } = 9.52 ; ;




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