9 25 28 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 25   c = 28

Area: T = 110.7977111876
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 18.45552071689° = 18°27'19″ = 0.32221041292 rad
Angle ∠ B = β = 61.56331098511° = 61°33'47″ = 1.07444789647 rad
Angle ∠ C = γ = 99.98216829799° = 99°58'54″ = 1.74550095597 rad

Height: ha = 24.62215804168
Height: hb = 8.86437689501
Height: hc = 7.91440794197

Median: ma = 26.15881727191
Median: mb = 16.62107701386
Median: mc = 12.53299640861

Inradius: r = 3.57441003831
Circumradius: R = 14.21551719782

Vertex coordinates: A[28; 0] B[0; 0] C[4.28657142857; 7.91440794197]
Centroid: CG[10.76219047619; 2.63880264732]
Coordinates of the circumscribed circle: U[14; -2.46439631429]
Coordinates of the inscribed circle: I[6; 3.57441003831]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.5454792831° = 161°32'41″ = 0.32221041292 rad
∠ B' = β' = 118.4376890149° = 118°26'13″ = 1.07444789647 rad
∠ C' = γ' = 80.01883170201° = 80°1'6″ = 1.74550095597 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 = 25 ; ; c = 28 ; ;

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

p = a+b+c = 9+25+28 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-9)(31-25)(31-28) } ; ; T = sqrt{ 12276 } = 110.8 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 110.8 }{ 9 } = 24.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 110.8 }{ 25 } = 8.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 110.8 }{ 28 } = 7.91 ; ;

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**2-25**2-28**2 }{ 2 * 25 * 28 } ) = 18° 27'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-9**2-28**2 }{ 2 * 9 * 28 } ) = 61° 33'47" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-9**2-25**2 }{ 2 * 25 * 9 } ) = 99° 58'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 110.8 }{ 31 } = 3.57 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 18° 27'19" } = 14.22 ; ;




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