9 17 24 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 17   c = 24

Area: T = 56.56985424949
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 16.09989339511° = 16°5'56″ = 0.28109794035 rad
Angle ∠ B = β = 31.58663380965° = 31°35'11″ = 0.55112855984 rad
Angle ∠ C = γ = 132.3154727952° = 132°18'53″ = 2.30993276517 rad

Height: ha = 12.57107872211
Height: hb = 6.65551226465
Height: hc = 4.71440452079

Median: ma = 20.30439405042
Median: mb = 16.00878105936
Median: mc = 6.40331242374

Inradius: r = 2.26327416998
Circumradius: R = 16.22881006282

Vertex coordinates: A[24; 0] B[0; 0] C[7.66766666667; 4.71440452079]
Centroid: CG[10.55655555556; 1.57113484026]
Coordinates of the circumscribed circle: U[12; -10.92547997693]
Coordinates of the inscribed circle: I[8; 2.26327416998]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.9011066049° = 163°54'4″ = 0.28109794035 rad
∠ B' = β' = 148.4143661903° = 148°24'49″ = 0.55112855984 rad
∠ C' = γ' = 47.68552720476° = 47°41'7″ = 2.30993276517 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 = 24 ; ;

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

p = a+b+c = 9+17+24 = 50 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 50 }{ 2 } = 25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25 * (25-9)(25-17)(25-24) } ; ; T = sqrt{ 3200 } = 56.57 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 56.57 }{ 9 } = 12.57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 56.57 }{ 17 } = 6.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 56.57 }{ 24 } = 4.71 ; ;

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**2-24**2 }{ 2 * 17 * 24 } ) = 16° 5'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-9**2-24**2 }{ 2 * 9 * 24 } ) = 31° 35'11" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-9**2-17**2 }{ 2 * 17 * 9 } ) = 132° 18'53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 56.57 }{ 25 } = 2.26 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 16° 5'56" } = 16.23 ; ;




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