5 24 25 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 24   c = 25

Area: T = 59.69992462264
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 11.47883409545° = 11°28'42″ = 0.22003348423 rad
Angle ∠ B = β = 72.78224885682° = 72°46'57″ = 1.27702940633 rad
Angle ∠ C = γ = 95.73991704773° = 95°44'21″ = 1.6710963748 rad

Height: ha = 23.88796984906
Height: hb = 4.97549371855
Height: hc = 4.77659396981

Median: ma = 24.37772434865
Median: mb = 13.45436240471
Median: mc = 12.01104121495

Inradius: r = 2.21110831936
Circumradius: R = 12.56329726907

Vertex coordinates: A[25; 0] B[0; 0] C[1.48; 4.77659396981]
Centroid: CG[8.82766666667; 1.59219798994]
Coordinates of the circumscribed circle: U[12.5; -1.25662972691]
Coordinates of the inscribed circle: I[3; 2.21110831936]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.5221659045° = 168°31'18″ = 0.22003348423 rad
∠ B' = β' = 107.2187511432° = 107°13'3″ = 1.27702940633 rad
∠ C' = γ' = 84.26108295227° = 84°15'39″ = 1.6710963748 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 = 5 ; ; b = 24 ; ; c = 25 ; ;

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

p = a+b+c = 5+24+25 = 54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54 }{ 2 } = 27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27 * (27-5)(27-24)(27-25) } ; ; T = sqrt{ 3564 } = 59.7 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 59.7 }{ 5 } = 23.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 59.7 }{ 24 } = 4.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 59.7 }{ 25 } = 4.78 ; ;

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{ 5**2-24**2-25**2 }{ 2 * 24 * 25 } ) = 11° 28'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-5**2-25**2 }{ 2 * 5 * 25 } ) = 72° 46'57" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-5**2-24**2 }{ 2 * 24 * 5 } ) = 95° 44'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 59.7 }{ 27 } = 2.21 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 11° 28'42" } = 12.56 ; ;




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