25 28 29 triangle

Acute scalene triangle.

Sides: a = 25   b = 28   c = 29

Area: T = 319.989998437
Perimeter: p = 82
Semiperimeter: s = 41

Angle ∠ A = α = 51.99325780701° = 51°59'33″ = 0.90774416739 rad
Angle ∠ B = β = 61.94333176341° = 61°56'36″ = 1.08111148423 rad
Angle ∠ C = γ = 66.06441042958° = 66°3'51″ = 1.15330361373 rad

Height: ha = 25.59219987496
Height: hb = 22.85499988836
Height: hc = 22.06220678876

Median: ma = 25.61773769149
Median: mb = 23.17332604525
Median: mc = 22.23217340754

Inradius: r = 7.80224386432
Circumradius: R = 15.8644333379

Vertex coordinates: A[29; 0] B[0; 0] C[11.75986206897; 22.06220678876]
Centroid: CG[13.58662068966; 7.35440226292]
Coordinates of the circumscribed circle: U[14.5; 6.43663866852]
Coordinates of the inscribed circle: I[13; 7.80224386432]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.007742193° = 128°27″ = 0.90774416739 rad
∠ B' = β' = 118.0576682366° = 118°3'24″ = 1.08111148423 rad
∠ C' = γ' = 113.9365895704° = 113°56'9″ = 1.15330361373 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 = 25 ; ; b = 28 ; ; c = 29 ; ;

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

p = a+b+c = 25+28+29 = 82 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 82 }{ 2 } = 41 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 41 * (41-25)(41-28)(41-29) } ; ; T = sqrt{ 102336 } = 319.9 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 319.9 }{ 25 } = 25.59 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 319.9 }{ 28 } = 22.85 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 319.9 }{ 29 } = 22.06 ; ;

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{ 25**2-28**2-29**2 }{ 2 * 28 * 29 } ) = 51° 59'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-25**2-29**2 }{ 2 * 25 * 29 } ) = 61° 56'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-25**2-28**2 }{ 2 * 28 * 25 } ) = 66° 3'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 319.9 }{ 41 } = 7.8 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 25 }{ 2 * sin 51° 59'33" } = 15.86 ; ;




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