10 24 25 triangle

Acute scalene triangle.

Sides: a = 10   b = 24   c = 25

Area: T = 119.3210733739
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 23.43767071991° = 23°26'12″ = 0.40990477064 rad
Angle ∠ B = β = 72.66224819825° = 72°39'45″ = 1.26881995533 rad
Angle ∠ C = γ = 83.90108108185° = 83°54'3″ = 1.46443453939 rad

Height: ha = 23.86441467478
Height: hb = 9.94333944782
Height: hc = 9.54656586991

Median: ma = 23.99895810718
Median: mb = 14.78217454991
Median: mc = 13.48114687627

Inradius: r = 4.04547706352
Circumradius: R = 12.57111597054

Vertex coordinates: A[25; 0] B[0; 0] C[2.98; 9.54656586991]
Centroid: CG[9.32766666667; 3.1821886233]
Coordinates of the circumscribed circle: U[12.5; 1.33656857187]
Coordinates of the inscribed circle: I[5.5; 4.04547706352]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.5633292801° = 156°33'48″ = 0.40990477064 rad
∠ B' = β' = 107.3387518018° = 107°20'15″ = 1.26881995533 rad
∠ C' = γ' = 96.09991891815° = 96°5'57″ = 1.46443453939 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 = 10 ; ; b = 24 ; ; c = 25 ; ;

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

p = a+b+c = 10+24+25 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-10)(29.5-24)(29.5-25) } ; ; T = sqrt{ 14237.44 } = 119.32 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 119.32 }{ 10 } = 23.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 119.32 }{ 24 } = 9.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 119.32 }{ 25 } = 9.55 ; ;

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{ 10**2-24**2-25**2 }{ 2 * 24 * 25 } ) = 23° 26'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-10**2-25**2 }{ 2 * 10 * 25 } ) = 72° 39'45" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-10**2-24**2 }{ 2 * 24 * 10 } ) = 83° 54'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 119.32 }{ 29.5 } = 4.04 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 23° 26'12" } = 12.57 ; ;




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