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

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 = 6.7 ; ; 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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 6.7**2-6.6**2-11.5**2 }{ 2 * 6.6 * 11.5 } ) = 30° 24'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 6.6**2-6.7**2-11.5**2 }{ 2 * 6.7 * 11.5 } ) = 29° 54'24" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11.5**2-6.7**2-6.6**2 }{ 2 * 6.6 * 6.7 } ) = 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 ; ;




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