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

Calculate another triangle


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 = 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 ; ;
Calculate another triangle


Look also our friend's collection of math examples and problems:

See more information about triangles or more details on solving triangles.