11 25 29 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 25   c = 29

Area: T = 135.4333332308
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 21.93883785037° = 21°56'18″ = 0.38328969374 rad
Angle ∠ B = β = 58.11551950233° = 58°6'55″ = 1.01443014986 rad
Angle ∠ C = γ = 99.9466426473° = 99°56'47″ = 1.74443942176 rad

Height: ha = 24.62442422378
Height: hb = 10.83546665846
Height: hc = 9.34402298143

Median: ma = 26.50994322836
Median: mb = 18.02108212909
Median: mc = 12.75773508222

Inradius: r = 4.16771794556
Circumradius: R = 14.72112651865

Vertex coordinates: A[29; 0] B[0; 0] C[5.81103448276; 9.34402298143]
Centroid: CG[11.60334482759; 3.11334099381]
Coordinates of the circumscribed circle: U[14.5; -2.54327639868]
Coordinates of the inscribed circle: I[7.5; 4.16771794556]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.0621621496° = 158°3'42″ = 0.38328969374 rad
∠ B' = β' = 121.8854804977° = 121°53'5″ = 1.01443014986 rad
∠ C' = γ' = 80.0543573527° = 80°3'13″ = 1.74443942176 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 = 25 ; ; c = 29 ; ;

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

p = a+b+c = 11+25+29 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-11)(32.5-25)(32.5-29) } ; ; T = sqrt{ 18342.19 } = 135.43 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 135.43 }{ 11 } = 24.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 135.43 }{ 25 } = 10.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 135.43 }{ 29 } = 9.34 ; ;

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**2-25**2-29**2 }{ 2 * 25 * 29 } ) = 21° 56'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-11**2-29**2 }{ 2 * 11 * 29 } ) = 58° 6'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-11**2-25**2 }{ 2 * 25 * 11 } ) = 99° 56'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 135.43 }{ 32.5 } = 4.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 21° 56'18" } = 14.72 ; ;




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