13 14 25 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 14   c = 25

Area: T = 63.68767333124
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 21.34113905316° = 21°20'29″ = 0.37224775317 rad
Angle ∠ B = β = 23.07439180656° = 23°4'26″ = 0.40327158416 rad
Angle ∠ C = γ = 135.5854691403° = 135°35'5″ = 2.36663992803 rad

Height: ha = 9.79879589711
Height: hb = 9.09881047589
Height: hc = 5.0954938665

Median: ma = 19.19898410624
Median: mb = 18.65547581062
Median: mc = 5.1233475383

Inradius: r = 2.44994897428
Circumradius: R = 17.86108627078

Vertex coordinates: A[25; 0] B[0; 0] C[11.96; 5.0954938665]
Centroid: CG[12.32; 1.69883128883]
Coordinates of the circumscribed circle: U[12.5; -12.7587759077]
Coordinates of the inscribed circle: I[12; 2.44994897428]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.6598609468° = 158°39'31″ = 0.37224775317 rad
∠ B' = β' = 156.9266081934° = 156°55'34″ = 0.40327158416 rad
∠ C' = γ' = 44.41553085972° = 44°24'55″ = 2.36663992803 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 = 14 ; ; c = 25 ; ;

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

p = a+b+c = 13+14+25 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-13)(26-14)(26-25) } ; ; T = sqrt{ 4056 } = 63.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 63.69 }{ 13 } = 9.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 63.69 }{ 14 } = 9.1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 63.69 }{ 25 } = 5.09 ; ;

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**2-14**2-25**2 }{ 2 * 14 * 25 } ) = 21° 20'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-13**2-25**2 }{ 2 * 13 * 25 } ) = 23° 4'26" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-13**2-14**2 }{ 2 * 14 * 13 } ) = 135° 35'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 63.69 }{ 26 } = 2.45 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 21° 20'29" } = 17.86 ; ;




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