5 23 25 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 23   c = 25

Area: T = 54.69217498349
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 10.96663338755° = 10°57'59″ = 0.1911398633 rad
Angle ∠ B = β = 61.05330241136° = 61°3'11″ = 1.06655762891 rad
Angle ∠ C = γ = 107.9810642011° = 107°58'50″ = 1.88546177315 rad

Height: ha = 21.87766999339
Height: hb = 4.75658043335
Height: hc = 4.37553399868

Median: ma = 23.89903746308
Median: mb = 13.88334433769
Median: mc = 10.98986304879

Inradius: r = 2.06438396164
Circumradius: R = 13.14218358742

Vertex coordinates: A[25; 0] B[0; 0] C[2.42; 4.37553399868]
Centroid: CG[9.14; 1.45884466623]
Coordinates of the circumscribed circle: U[12.5; -4.05768275959]
Coordinates of the inscribed circle: I[3.5; 2.06438396164]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.0343666124° = 169°2'1″ = 0.1911398633 rad
∠ B' = β' = 118.9476975886° = 118°56'49″ = 1.06655762891 rad
∠ C' = γ' = 72.01993579891° = 72°1'10″ = 1.88546177315 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 = 23 ; ; c = 25 ; ;

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

p = a+b+c = 5+23+25 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-5)(26.5-23)(26.5-25) } ; ; T = sqrt{ 2991.19 } = 54.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 54.69 }{ 5 } = 21.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 54.69 }{ 23 } = 4.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 54.69 }{ 25 } = 4.38 ; ;

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**2-23**2-25**2 }{ 2 * 23 * 25 } ) = 10° 57'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-5**2-25**2 }{ 2 * 5 * 25 } ) = 61° 3'11" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-5**2-23**2 }{ 2 * 23 * 5 } ) = 107° 58'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 54.69 }{ 26.5 } = 2.06 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 10° 57'59" } = 13.14 ; ;




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