17 24 25 triangle

Acute scalene triangle.

Sides: a = 17   b = 24   c = 25

Area: T = 194.9776921711
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 40.53658021113° = 40°32'9″ = 0.70774832118 rad
Angle ∠ B = β = 66.56988330653° = 66°34'8″ = 1.16218453162 rad
Angle ∠ C = γ = 72.89553648234° = 72°53'43″ = 1.27222641256 rad

Height: ha = 22.93884613778
Height: hb = 16.24880768093
Height: hc = 15.59881537369

Median: ma = 22.98436898691
Median: mb = 17.6921806013
Median: mc = 16.62107701386

Inradius: r = 5.9088391567
Circumradius: R = 13.07884709166

Vertex coordinates: A[25; 0] B[0; 0] C[6.76; 15.59881537369]
Centroid: CG[10.58766666667; 5.1999384579]
Coordinates of the circumscribed circle: U[12.5; 3.84766090931]
Coordinates of the inscribed circle: I[9; 5.9088391567]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.4644197889° = 139°27'51″ = 0.70774832118 rad
∠ B' = β' = 113.4311166935° = 113°25'52″ = 1.16218453162 rad
∠ C' = γ' = 107.1054635177° = 107°6'17″ = 1.27222641256 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 = 17 ; ; b = 24 ; ; c = 25 ; ;

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

p = a+b+c = 17+24+25 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-17)(33-24)(33-25) } ; ; T = sqrt{ 38016 } = 194.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 194.98 }{ 17 } = 22.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 194.98 }{ 24 } = 16.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 194.98 }{ 25 } = 15.6 ; ;

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{ 17**2-24**2-25**2 }{ 2 * 24 * 25 } ) = 40° 32'9" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-17**2-25**2 }{ 2 * 17 * 25 } ) = 66° 34'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-17**2-24**2 }{ 2 * 24 * 17 } ) = 72° 53'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 194.98 }{ 33 } = 5.91 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 40° 32'9" } = 13.08 ; ;




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