22 27 29 triangle

Acute scalene triangle.

Sides: a = 22   b = 27   c = 29

Area: T = 282.0643822565
Perimeter: p = 78
Semiperimeter: s = 39

Angle ∠ A = α = 46.09332596507° = 46°5'36″ = 0.80444791439 rad
Angle ∠ B = β = 62.15547800217° = 62°9'17″ = 1.08548055572 rad
Angle ∠ C = γ = 71.75219603276° = 71°45'7″ = 1.25223079525 rad

Height: ha = 25.64221656877
Height: hb = 20.89436164863
Height: hc = 19.45326774183

Median: ma = 25.76881974535
Median: mb = 21.91546070008
Median: mc = 19.90660292374

Inradius: r = 7.23224057068
Circumradius: R = 15.26878211649

Vertex coordinates: A[29; 0] B[0; 0] C[10.2765862069; 19.45326774183]
Centroid: CG[13.0921954023; 6.48442258061]
Coordinates of the circumscribed circle: U[14.5; 4.781083289]
Coordinates of the inscribed circle: I[12; 7.23224057068]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.9076740349° = 133°54'24″ = 0.80444791439 rad
∠ B' = β' = 117.8455219978° = 117°50'43″ = 1.08548055572 rad
∠ C' = γ' = 108.2488039672° = 108°14'53″ = 1.25223079525 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 = 22 ; ; b = 27 ; ; c = 29 ; ;

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

p = a+b+c = 22+27+29 = 78 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 78 }{ 2 } = 39 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 39 * (39-22)(39-27)(39-29) } ; ; T = sqrt{ 79560 } = 282.06 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 282.06 }{ 22 } = 25.64 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 282.06 }{ 27 } = 20.89 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 282.06 }{ 29 } = 19.45 ; ;

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{ 22**2-27**2-29**2 }{ 2 * 27 * 29 } ) = 46° 5'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-22**2-29**2 }{ 2 * 22 * 29 } ) = 62° 9'17" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-22**2-27**2 }{ 2 * 27 * 22 } ) = 71° 45'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 282.06 }{ 39 } = 7.23 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 46° 5'36" } = 15.27 ; ;




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