5 8 11 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 8   c = 11

Area: T = 18.33303027798
Perimeter: p = 24
Semiperimeter: s = 12

Angle ∠ A = α = 24.62199773287° = 24°37'12″ = 0.43296996662 rad
Angle ∠ B = β = 41.80218441931° = 41°48'7″ = 0.73295798146 rad
Angle ∠ C = γ = 113.5788178478° = 113°34'41″ = 1.98223131729 rad

Height: ha = 7.33221211119
Height: hb = 4.5832575695
Height: hc = 3.33327823236

Median: ma = 9.28770878105
Median: mb = 7.55498344353
Median: mc = 3.77549172176

Inradius: r = 1.52875252317
Circumradius: R = 6.00109919815

Vertex coordinates: A[11; 0] B[0; 0] C[3.72772727273; 3.33327823236]
Centroid: CG[4.90990909091; 1.11109274412]
Coordinates of the circumscribed circle: U[5.5; -2.44003967926]
Coordinates of the inscribed circle: I[4; 1.52875252317]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.3880022671° = 155°22'48″ = 0.43296996662 rad
∠ B' = β' = 138.1988155807° = 138°11'53″ = 0.73295798146 rad
∠ C' = γ' = 66.42218215218° = 66°25'19″ = 1.98223131729 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 = 8 ; ; c = 11 ; ;

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

p = a+b+c = 5+8+11 = 24 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 24 }{ 2 } = 12 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12 * (12-5)(12-8)(12-11) } ; ; T = sqrt{ 336 } = 18.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 18.33 }{ 5 } = 7.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 18.33 }{ 8 } = 4.58 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 18.33 }{ 11 } = 3.33 ; ;

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**2-8**2-11**2 }{ 2 * 8 * 11 } ) = 24° 37'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8**2-5**2-11**2 }{ 2 * 5 * 11 } ) = 41° 48'7" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11**2-5**2-8**2 }{ 2 * 8 * 5 } ) = 113° 34'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 18.33 }{ 12 } = 1.53 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 24° 37'12" } = 6 ; ;




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