9 22 25 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 22   c = 25

Area: T = 97.85770385818
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 20.84551663601° = 20°50'43″ = 0.36438167861 rad
Angle ∠ B = β = 60.44400916213° = 60°26'24″ = 1.0554878599 rad
Angle ∠ C = γ = 98.71547420186° = 98°42'53″ = 1.72328972685 rad

Height: ha = 21.74660085737
Height: hb = 8.89660944165
Height: hc = 7.82985630865

Median: ma = 23.11438486627
Median: mb = 15.23215462117
Median: mc = 11.23661025271

Inradius: r = 3.49548942351
Circumradius: R = 12.64659988769

Vertex coordinates: A[25; 0] B[0; 0] C[4.44; 7.82985630865]
Centroid: CG[9.81333333333; 2.61095210288]
Coordinates of the circumscribed circle: U[12.5; -1.91660604359]
Coordinates of the inscribed circle: I[6; 3.49548942351]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.155483364° = 159°9'17″ = 0.36438167861 rad
∠ B' = β' = 119.5659908379° = 119°33'36″ = 1.0554878599 rad
∠ C' = γ' = 81.28552579814° = 81°17'7″ = 1.72328972685 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 = 9 ; ; b = 22 ; ; c = 25 ; ;

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

p = a+b+c = 9+22+25 = 56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56 }{ 2 } = 28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28 * (28-9)(28-22)(28-25) } ; ; T = sqrt{ 9576 } = 97.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 97.86 }{ 9 } = 21.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 97.86 }{ 22 } = 8.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 97.86 }{ 25 } = 7.83 ; ;

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{ 9**2-22**2-25**2 }{ 2 * 22 * 25 } ) = 20° 50'43" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-9**2-25**2 }{ 2 * 9 * 25 } ) = 60° 26'24" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-9**2-22**2 }{ 2 * 22 * 9 } ) = 98° 42'53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 97.86 }{ 28 } = 3.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 20° 50'43" } = 12.65 ; ;




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