6.41 6.41 12.19 triangle

Obtuse isosceles triangle.

Sides: a = 6.41   b = 6.41   c = 12.19

Area: T = 12.0976809317
Perimeter: p = 25.01
Semiperimeter: s = 12.505

Angle ∠ A = α = 18.03767648456° = 18°2'12″ = 0.3154800933 rad
Angle ∠ B = β = 18.03767648456° = 18°2'12″ = 0.3154800933 rad
Angle ∠ C = γ = 143.9266470309° = 143°55'35″ = 2.51219907877 rad

Height: ha = 3.77443554811
Height: hb = 3.77443554811
Height: hc = 1.98547103063

Median: ma = 9.1966198943
Median: mb = 9.1966198943
Median: mc = 1.98547103063

Inradius: r = 0.96773578022
Circumradius: R = 10.35111580177

Vertex coordinates: A[12.19; 0] B[0; 0] C[6.095; 1.98547103063]
Centroid: CG[6.095; 0.66215701021]
Coordinates of the circumscribed circle: U[6.095; -8.36664477114]
Coordinates of the inscribed circle: I[6.095; 0.96773578022]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.9633235154° = 161°57'48″ = 0.3154800933 rad
∠ B' = β' = 161.9633235154° = 161°57'48″ = 0.3154800933 rad
∠ C' = γ' = 36.07435296912° = 36°4'25″ = 2.51219907877 rad

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How did we calculate this triangle?

a = 6.41 ; ; b = 6.41 ; ; c = 12.19 ; ;

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

p = a+b+c = 6.41+6.41+12.19 = 25.01 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 25.01 }{ 2 } = 12.51 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.51 * (12.51-6.41)(12.51-6.41)(12.51-12.19) } ; ; T = sqrt{ 146.33 } = 12.1 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 12.1 }{ 6.41 } = 3.77 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 12.1 }{ 6.41 } = 3.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 12.1 }{ 12.19 } = 1.98 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 6.41**2+12.19**2-6.41**2 }{ 2 * 6.41 * 12.19 } ) = 18° 2'12" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6.41**2+12.19**2-6.41**2 }{ 2 * 6.41 * 12.19 } ) = 18° 2'12" ; ; gamma = 180° - alpha - beta = 180° - 18° 2'12" - 18° 2'12" = 143° 55'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 12.1 }{ 12.51 } = 0.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6.41 }{ 2 * sin 18° 2'12" } = 10.35 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.41**2+2 * 12.19**2 - 6.41**2 } }{ 2 } = 9.196 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.19**2+2 * 6.41**2 - 6.41**2 } }{ 2 } = 9.196 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.41**2+2 * 6.41**2 - 12.19**2 } }{ 2 } = 1.985 ; ;
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