6.7 6.6 11.5 triangle

Obtuse scalene triangle.

Sides: a = 6.7   b = 6.6   c = 11.5

Area: T = 19.20880608079
Perimeter: p = 24.8
Semiperimeter: s = 12.4

Angle ∠ A = α = 30.40771410713° = 30°24'26″ = 0.53107047278 rad
Angle ∠ B = β = 29.90765548434° = 29°54'24″ = 0.52219678499 rad
Angle ∠ C = γ = 119.6866304085° = 119°41'11″ = 2.08989200758 rad

Height: ha = 5.73437494949
Height: hb = 5.82106244872
Height: hc = 3.34105323144

Median: ma = 8.75768544581
Median: mb = 8.81436258146
Median: mc = 3.34110327745

Inradius: r = 1.54990371619
Circumradius: R = 6.6198705619

Vertex coordinates: A[11.5; 0] B[0; 0] C[5.8087826087; 3.34105323144]
Centroid: CG[5.76992753623; 1.11435107715]
Coordinates of the circumscribed circle: U[5.75; -3.27879206933]
Coordinates of the inscribed circle: I[5.8; 1.54990371619]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.5932858929° = 149°35'34″ = 0.53107047278 rad
∠ B' = β' = 150.0933445157° = 150°5'36″ = 0.52219678499 rad
∠ C' = γ' = 60.31436959147° = 60°18'49″ = 2.08989200758 rad

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How did we calculate this triangle?

a = 6.7 ; ; b = 6.6 ; ; c = 11.5 ; ;

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

p = a+b+c = 6.7+6.6+11.5 = 24.8 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 24.8 }{ 2 } = 12.4 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.4 * (12.4-6.7)(12.4-6.6)(12.4-11.5) } ; ; T = sqrt{ 368.95 } = 19.21 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 19.21 }{ 6.7 } = 5.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 19.21 }{ 6.6 } = 5.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 19.21 }{ 11.5 } = 3.34 ; ;

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{ 6.6**2+11.5**2-6.7**2 }{ 2 * 6.6 * 11.5 } ) = 30° 24'26" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6.7**2+11.5**2-6.6**2 }{ 2 * 6.7 * 11.5 } ) = 29° 54'24" ; ; gamma = 180° - alpha - beta = 180° - 30° 24'26" - 29° 54'24" = 119° 41'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 19.21 }{ 12.4 } = 1.55 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6.7 }{ 2 * sin 30° 24'26" } = 6.62 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.6**2+2 * 11.5**2 - 6.7**2 } }{ 2 } = 8.757 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 11.5**2+2 * 6.7**2 - 6.6**2 } }{ 2 } = 8.814 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.6**2+2 * 6.7**2 - 11.5**2 } }{ 2 } = 3.341 ; ;
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