25 27 29 triangle

Acute scalene triangle.

Sides: a = 25   b = 27   c = 29

Area: T = 312.1832939156
Perimeter: p = 81
Semiperimeter: s = 40.5

Angle ∠ A = α = 52.88327365328° = 52°52'58″ = 0.923297787 rad
Angle ∠ B = β = 59.4510946125° = 59°27'3″ = 1.03876147533 rad
Angle ∠ C = γ = 67.66663173422° = 67°39'59″ = 1.18110000303 rad

Height: ha = 24.97546351325
Height: hb = 23.12546621597
Height: hc = 21.53298578728

Median: ma = 25.07548878362
Median: mb = 23.46880634054
Median: mc = 21.60443977005

Inradius: r = 7.70882207199
Circumradius: R = 15.67659046898

Vertex coordinates: A[29; 0] B[0; 0] C[12.70768965517; 21.53298578728]
Centroid: CG[13.90222988506; 7.17766192909]
Coordinates of the circumscribed circle: U[14.5; 5.95768437821]
Coordinates of the inscribed circle: I[13.5; 7.70882207199]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.1177263467° = 127°7'2″ = 0.923297787 rad
∠ B' = β' = 120.5499053875° = 120°32'57″ = 1.03876147533 rad
∠ C' = γ' = 112.3343682658° = 112°20'1″ = 1.18110000303 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 = 27 ; ; c = 29 ; ;

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

p = a+b+c = 25+27+29 = 81 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 81 }{ 2 } = 40.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 40.5 * (40.5-25)(40.5-27)(40.5-29) } ; ; T = sqrt{ 97458.19 } = 312.18 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 312.18 }{ 25 } = 24.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 312.18 }{ 27 } = 23.12 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 312.18 }{ 29 } = 21.53 ; ;

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**2-27**2-29**2 }{ 2 * 27 * 29 } ) = 52° 52'58" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-25**2-29**2 }{ 2 * 25 * 29 } ) = 59° 27'3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-25**2-27**2 }{ 2 * 27 * 25 } ) = 67° 39'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 312.18 }{ 40.5 } = 7.71 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 25 }{ 2 * sin 52° 52'58" } = 15.68 ; ;




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