9 17 23 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 17   c = 23

Area: T = 65.36219728894
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 19.53219431377° = 19°31'55″ = 0.34108967171 rad
Angle ∠ B = β = 39.16221067955° = 39°9'44″ = 0.68435077056 rad
Angle ∠ C = γ = 121.3065950067° = 121°18'21″ = 2.11771882309 rad

Height: ha = 14.52548828643
Height: hb = 7.69896438693
Height: hc = 5.68436498165

Median: ma = 19.71767441531
Median: mb = 15.25661463024
Median: mc = 7.26329195232

Inradius: r = 2.66878356281
Circumradius: R = 13.465966104

Vertex coordinates: A[23; 0] B[0; 0] C[6.97882608696; 5.68436498165]
Centroid: CG[9.99327536232; 1.89545499388]
Coordinates of the circumscribed circle: U[11.5; -6.99437454424]
Coordinates of the inscribed circle: I[7.5; 2.66878356281]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.4688056862° = 160°28'5″ = 0.34108967171 rad
∠ B' = β' = 140.8387893204° = 140°50'16″ = 0.68435077056 rad
∠ C' = γ' = 58.69440499332° = 58°41'39″ = 2.11771882309 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 = 23 ; ;

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

p = a+b+c = 9+17+23 = 49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49 }{ 2 } = 24.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.5 * (24.5-9)(24.5-17)(24.5-23) } ; ; T = sqrt{ 4272.19 } = 65.36 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 65.36 }{ 9 } = 14.52 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 65.36 }{ 17 } = 7.69 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 65.36 }{ 23 } = 5.68 ; ;

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**2-23**2 }{ 2 * 17 * 23 } ) = 19° 31'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-9**2-23**2 }{ 2 * 9 * 23 } ) = 39° 9'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-9**2-17**2 }{ 2 * 17 * 9 } ) = 121° 18'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 65.36 }{ 24.5 } = 2.67 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 19° 31'55" } = 13.46 ; ;




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