22 28 29 triangle

Acute scalene triangle.

Sides: a = 22   b = 28   c = 29

Area: T = 288.9099047106
Perimeter: p = 79
Semiperimeter: s = 39.5

Angle ∠ A = α = 45.3655134224° = 45°21'54″ = 0.79217709578 rad
Angle ∠ B = β = 64.91438068357° = 64°54'50″ = 1.13329596593 rad
Angle ∠ C = γ = 69.72110589402° = 69°43'16″ = 1.21768620365 rad

Height: ha = 26.26444588279
Height: hb = 20.63663605076
Height: hc = 19.92547618694

Median: ma = 26.29663875846
Median: mb = 21.59986110665
Median: mc = 20.58551888502

Inradius: r = 7.31441530913
Circumradius: R = 15.45881521234

Vertex coordinates: A[29; 0] B[0; 0] C[9.32875862069; 19.92547618694]
Centroid: CG[12.7765862069; 6.64215872898]
Coordinates of the circumscribed circle: U[14.5; 5.35876549973]
Coordinates of the inscribed circle: I[11.5; 7.31441530913]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.6354865776° = 134°38'6″ = 0.79217709578 rad
∠ B' = β' = 115.0866193164° = 115°5'10″ = 1.13329596593 rad
∠ C' = γ' = 110.279894106° = 110°16'44″ = 1.21768620365 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 = 28 ; ; c = 29 ; ;

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

p = a+b+c = 22+28+29 = 79 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 79 }{ 2 } = 39.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 39.5 * (39.5-22)(39.5-28)(39.5-29) } ; ; T = sqrt{ 83468.44 } = 288.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 288.91 }{ 22 } = 26.26 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 288.91 }{ 28 } = 20.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 288.91 }{ 29 } = 19.92 ; ;

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**2-28**2-29**2 }{ 2 * 28 * 29 } ) = 45° 21'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-22**2-29**2 }{ 2 * 22 * 29 } ) = 64° 54'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-22**2-28**2 }{ 2 * 28 * 22 } ) = 69° 43'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 288.91 }{ 39.5 } = 7.31 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 45° 21'54" } = 15.46 ; ;




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