11 22 25 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 22   c = 25

Area: T = 120.8976650078
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 26.08799049389° = 26°4'48″ = 0.45551802098 rad
Angle ∠ B = β = 61.5521826557° = 61°33'7″ = 1.0744282034 rad
Angle ∠ C = γ = 92.36882685041° = 92°22'6″ = 1.61221304098 rad

Height: ha = 21.9811209105
Height: hb = 10.99106045525
Height: hc = 9.67217320062

Median: ma = 22.89765062837
Median: mb = 15.87545078664
Median: mc = 12.09333866224

Inradius: r = 4.16988500027
Circumradius: R = 12.51106857719

Vertex coordinates: A[25; 0] B[0; 0] C[5.24; 9.67217320062]
Centroid: CG[10.08; 3.22439106687]
Coordinates of the circumscribed circle: U[12.5; -0.51769704864]
Coordinates of the inscribed circle: I[7; 4.16988500027]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.9220095061° = 153°55'12″ = 0.45551802098 rad
∠ B' = β' = 118.4488173443° = 118°26'53″ = 1.0744282034 rad
∠ C' = γ' = 87.63217314959° = 87°37'54″ = 1.61221304098 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 = 22 ; ; c = 25 ; ;

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

p = a+b+c = 11+22+25 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-11)(29-22)(29-25) } ; ; T = sqrt{ 14616 } = 120.9 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 120.9 }{ 11 } = 21.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 120.9 }{ 22 } = 10.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 120.9 }{ 25 } = 9.67 ; ;

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**2-22**2-25**2 }{ 2 * 22 * 25 } ) = 26° 4'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-11**2-25**2 }{ 2 * 11 * 25 } ) = 61° 33'7" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-11**2-22**2 }{ 2 * 22 * 11 } ) = 92° 22'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 120.9 }{ 29 } = 4.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 26° 4'48" } = 12.51 ; ;




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