13 17 25 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 17   c = 25

Area: T = 102.3099273773
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 28.78105000852° = 28°46'50″ = 0.50223144869 rad
Angle ∠ B = β = 39.02202878409° = 39°1'13″ = 0.68110324979 rad
Angle ∠ C = γ = 112.1999212074° = 112°11'57″ = 1.95882456688 rad

Height: ha = 15.74398882728
Height: hb = 12.03663851498
Height: hc = 8.18547419019

Median: ma = 20.36554118544
Median: mb = 18.02108212909
Median: mc = 8.52993610546

Inradius: r = 3.72203372281
Circumradius: R = 13.50107311562

Vertex coordinates: A[25; 0] B[0; 0] C[10.1; 8.18547419019]
Centroid: CG[11.7; 2.72882473006]
Coordinates of the circumscribed circle: U[12.5; -5.10109549844]
Coordinates of the inscribed circle: I[10.5; 3.72203372281]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.2199499915° = 151°13'10″ = 0.50223144869 rad
∠ B' = β' = 140.9879712159° = 140°58'47″ = 0.68110324979 rad
∠ C' = γ' = 67.80107879261° = 67°48'3″ = 1.95882456688 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 = 13 ; ; b = 17 ; ; c = 25 ; ;

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

p = a+b+c = 13+17+25 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-13)(27.5-17)(27.5-25) } ; ; T = sqrt{ 10467.19 } = 102.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 102.31 }{ 13 } = 15.74 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 102.31 }{ 17 } = 12.04 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 102.31 }{ 25 } = 8.18 ; ;

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{ 13**2-17**2-25**2 }{ 2 * 17 * 25 } ) = 28° 46'50" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-13**2-25**2 }{ 2 * 13 * 25 } ) = 39° 1'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-13**2-17**2 }{ 2 * 17 * 13 } ) = 112° 11'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 102.31 }{ 27.5 } = 3.72 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 28° 46'50" } = 13.5 ; ;




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