5 7 11 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 7   c = 11

Area: T = 12.96987123493
Perimeter: p = 23
Semiperimeter: s = 11.5

Angle ∠ A = α = 19.68550548247° = 19°41'6″ = 0.34435690201 rad
Angle ∠ B = β = 28.13875265744° = 28°8'15″ = 0.49110924821 rad
Angle ∠ C = γ = 132.1777418601° = 132°10'39″ = 2.30769311514 rad

Height: ha = 5.18774849397
Height: hb = 3.70553463855
Height: hc = 2.35879476999

Median: ma = 8.87441196746
Median: mb = 7.79442286341
Median: mc = 2.59880762114

Inradius: r = 1.12877141173
Circumradius: R = 7.42217082936

Vertex coordinates: A[11; 0] B[0; 0] C[4.40990909091; 2.35879476999]
Centroid: CG[5.13663636364; 0.78659825666]
Coordinates of the circumscribed circle: U[5.5; -4.98331469971]
Coordinates of the inscribed circle: I[4.5; 1.12877141173]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.3154945175° = 160°18'54″ = 0.34435690201 rad
∠ B' = β' = 151.8622473426° = 151°51'45″ = 0.49110924821 rad
∠ C' = γ' = 47.82325813991° = 47°49'21″ = 2.30769311514 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 = 5 ; ; b = 7 ; ; c = 11 ; ;

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

p = a+b+c = 5+7+11 = 23 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 23 }{ 2 } = 11.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.5 * (11.5-5)(11.5-7)(11.5-11) } ; ; T = sqrt{ 168.19 } = 12.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 12.97 }{ 5 } = 5.19 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 12.97 }{ 7 } = 3.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 12.97 }{ 11 } = 2.36 ; ;

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{ 5**2-7**2-11**2 }{ 2 * 7 * 11 } ) = 19° 41'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7**2-5**2-11**2 }{ 2 * 5 * 11 } ) = 28° 8'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11**2-5**2-7**2 }{ 2 * 7 * 5 } ) = 132° 10'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 12.97 }{ 11.5 } = 1.13 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 19° 41'6" } = 7.42 ; ;




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