9 23 30 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 23   c = 30

Area: T = 73.86547412505
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 12.36327726659° = 12°21'46″ = 0.21657710877 rad
Angle ∠ B = β = 33.17114519508° = 33°10'17″ = 0.57989510542 rad
Angle ∠ C = γ = 134.4665775383° = 134°27'57″ = 2.34768705117 rad

Height: ha = 16.41443869446
Height: hb = 6.42330209783
Height: hc = 4.92443160834

Median: ma = 26.34986242525
Median: mb = 18.92774932307
Median: mc = 8.944427191

Inradius: r = 2.38327335887
Circumradius: R = 21.01881471392

Vertex coordinates: A[30; 0] B[0; 0] C[7.53333333333; 4.92443160834]
Centroid: CG[12.51111111111; 1.64114386945]
Coordinates of the circumscribed circle: U[15; -14.72328566917]
Coordinates of the inscribed circle: I[8; 2.38327335887]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.6377227334° = 167°38'14″ = 0.21657710877 rad
∠ B' = β' = 146.8298548049° = 146°49'43″ = 0.57989510542 rad
∠ C' = γ' = 45.53442246167° = 45°32'3″ = 2.34768705117 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 = 23 ; ; c = 30 ; ;

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

p = a+b+c = 9+23+30 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-9)(31-23)(31-30) } ; ; T = sqrt{ 5456 } = 73.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 73.86 }{ 9 } = 16.41 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 73.86 }{ 23 } = 6.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 73.86 }{ 30 } = 4.92 ; ;

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**2-23**2-30**2 }{ 2 * 23 * 30 } ) = 12° 21'46" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-9**2-30**2 }{ 2 * 9 * 30 } ) = 33° 10'17" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-9**2-23**2 }{ 2 * 23 * 9 } ) = 134° 27'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 73.86 }{ 31 } = 2.38 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 12° 21'46" } = 21.02 ; ;




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