9 17 25 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 17   c = 25

Area: T = 42.2876966077
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 11.47883409545° = 11°28'42″ = 0.22003348423 rad
Angle ∠ B = β = 22.07989688074° = 22°4'44″ = 0.38553507011 rad
Angle ∠ C = γ = 146.4432690238° = 146°26'34″ = 2.55659071101 rad

Height: ha = 9.39771035727
Height: hb = 4.97549371855
Height: hc = 3.38329572862

Median: ma = 20.8998564544
Median: mb = 16.75655960801
Median: mc = 5.36219026474

Inradius: r = 1.65883123952
Circumradius: R = 22.61333508433

Vertex coordinates: A[25; 0] B[0; 0] C[8.34; 3.38329572862]
Centroid: CG[11.11333333333; 1.12876524287]
Coordinates of the circumscribed circle: U[12.5; -18.84444590361]
Coordinates of the inscribed circle: I[8.5; 1.65883123952]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.5221659045° = 168°31'18″ = 0.22003348423 rad
∠ B' = β' = 157.9211031193° = 157°55'16″ = 0.38553507011 rad
∠ C' = γ' = 33.55773097619° = 33°33'26″ = 2.55659071101 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 = 9 ; ; b = 17 ; ; c = 25 ; ;

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

p = a+b+c = 9+17+25 = 51 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 51 }{ 2 } = 25.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25.5 * (25.5-9)(25.5-17)(25.5-25) } ; ; T = sqrt{ 1788.19 } = 42.29 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 42.29 }{ 9 } = 9.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 42.29 }{ 17 } = 4.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 42.29 }{ 25 } = 3.38 ; ;

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{ 9**2-17**2-25**2 }{ 2 * 17 * 25 } ) = 11° 28'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-9**2-25**2 }{ 2 * 9 * 25 } ) = 22° 4'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-9**2-17**2 }{ 2 * 17 * 9 } ) = 146° 26'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 42.29 }{ 25.5 } = 1.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 11° 28'42" } = 22.61 ; ;




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