11 28 29 triangle

Acute scalene triangle.

Sides: a = 11   b = 28   c = 29

Area: T = 153.1676575988
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 22.16439137383° = 22°9'50″ = 0.38768332699 rad
Angle ∠ B = β = 73.879965638° = 73°47'59″ = 1.28880469907 rad
Angle ∠ C = γ = 84.03664298817° = 84°2'11″ = 1.46767123931 rad

Height: ha = 27.84884683615
Height: hb = 10.94404697135
Height: hc = 10.56332121371

Median: ma = 27.96987325419
Median: mb = 16.88219430161
Median: mc = 15.56443824163

Inradius: r = 4.50548992938
Circumradius: R = 14.5798898729

Vertex coordinates: A[29; 0] B[0; 0] C[3.06989655172; 10.56332121371]
Centroid: CG[10.69896551724; 3.52110707124]
Coordinates of the circumscribed circle: U[14.5; 1.5154690777]
Coordinates of the inscribed circle: I[6; 4.50548992938]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.8366086262° = 157°50'10″ = 0.38768332699 rad
∠ B' = β' = 106.220034362° = 106°12'1″ = 1.28880469907 rad
∠ C' = γ' = 95.96435701183° = 95°57'49″ = 1.46767123931 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 = 11 ; ; b = 28 ; ; c = 29 ; ;

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

p = a+b+c = 11+28+29 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-11)(34-28)(34-29) } ; ; T = sqrt{ 23460 } = 153.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 153.17 }{ 11 } = 27.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 153.17 }{ 28 } = 10.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 153.17 }{ 29 } = 10.56 ; ;

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{ 11**2-28**2-29**2 }{ 2 * 28 * 29 } ) = 22° 9'50" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-11**2-29**2 }{ 2 * 11 * 29 } ) = 73° 47'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-11**2-28**2 }{ 2 * 28 * 11 } ) = 84° 2'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 153.17 }{ 34 } = 4.5 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 22° 9'50" } = 14.58 ; ;




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