3 24 25 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 24   c = 25

Area: T = 34.58332329316
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 6.62196277953° = 6°37'11″ = 0.11655343003 rad
Angle ∠ B = β = 67.25327519916° = 67°15'10″ = 1.17437819533 rad
Angle ∠ C = γ = 106.1287620213° = 106°7'39″ = 1.85222764 rad

Height: ha = 23.05554886211
Height: hb = 2.88219360776
Height: hc = 2.76766586345

Median: ma = 24.45991496173
Median: mb = 13.1532946438
Median: mc = 11.67326175299

Inradius: r = 1.33301243435
Circumradius: R = 13.01220859692

Vertex coordinates: A[25; 0] B[0; 0] C[1.16; 2.76766586345]
Centroid: CG[8.72; 0.92222195448]
Coordinates of the circumscribed circle: U[12.5; -3.61444683248]
Coordinates of the inscribed circle: I[2; 1.33301243435]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.3880372205° = 173°22'49″ = 0.11655343003 rad
∠ B' = β' = 112.7477248008° = 112°44'50″ = 1.17437819533 rad
∠ C' = γ' = 73.87223797868° = 73°52'21″ = 1.85222764 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 = 3 ; ; b = 24 ; ; c = 25 ; ;

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

p = a+b+c = 3+24+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 * (26-3)(26-24)(26-25) } ; ; T = sqrt{ 1196 } = 34.58 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 34.58 }{ 3 } = 23.06 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 34.58 }{ 24 } = 2.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 34.58 }{ 25 } = 2.77 ; ;

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{ 3**2-24**2-25**2 }{ 2 * 24 * 25 } ) = 6° 37'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-3**2-25**2 }{ 2 * 3 * 25 } ) = 67° 15'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-3**2-24**2 }{ 2 * 24 * 3 } ) = 106° 7'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 34.58 }{ 26 } = 1.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 6° 37'11" } = 13.01 ; ;




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