4 8 11 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 8   c = 11

Area: T = 12.28656623753
Perimeter: p = 23
Semiperimeter: s = 11.5

Angle ∠ A = α = 16.2143633496° = 16°12'49″ = 0.28329812882 rad
Angle ∠ B = β = 33.9487926527° = 33°56'53″ = 0.59325030921 rad
Angle ∠ C = γ = 129.8388439977° = 129°50'18″ = 2.26661082733 rad

Height: ha = 6.14328311877
Height: hb = 3.07114155938
Height: hc = 2.23437567955

Median: ma = 9.40774438611
Median: mb = 7.24656883731
Median: mc = 3.12224989992

Inradius: r = 1.06883184674
Circumradius: R = 7.16328209625

Vertex coordinates: A[11; 0] B[0; 0] C[3.31881818182; 2.23437567955]
Centroid: CG[4.77327272727; 0.74545855985]
Coordinates of the circumscribed circle: U[5.5; -4.58986821791]
Coordinates of the inscribed circle: I[3.5; 1.06883184674]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.7866366504° = 163°47'11″ = 0.28329812882 rad
∠ B' = β' = 146.0522073473° = 146°3'7″ = 0.59325030921 rad
∠ C' = γ' = 50.1621560023° = 50°9'42″ = 2.26661082733 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 = 4 ; ; b = 8 ; ; c = 11 ; ;

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

p = a+b+c = 4+8+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 * (11.5-4)(11.5-8)(11.5-11) } ; ; T = sqrt{ 150.94 } = 12.29 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 12.29 }{ 4 } = 6.14 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 12.29 }{ 8 } = 3.07 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 12.29 }{ 11 } = 2.23 ; ;

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{ 4**2-8**2-11**2 }{ 2 * 8 * 11 } ) = 16° 12'49" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8**2-4**2-11**2 }{ 2 * 4 * 11 } ) = 33° 56'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11**2-4**2-8**2 }{ 2 * 8 * 4 } ) = 129° 50'18" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 12.29 }{ 11.5 } = 1.07 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 16° 12'49" } = 7.16 ; ;




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