11 17 24 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 17   c = 24

Area: T = 83.78554402626
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 24.25496286025° = 24°14'59″ = 0.42332358615 rad
Angle ∠ B = β = 39.40105687537° = 39°24'2″ = 0.68876696519 rad
Angle ∠ C = γ = 116.3549802644° = 116°20'59″ = 2.03106871402 rad

Height: ha = 15.23437164114
Height: hb = 9.85771106191
Height: hc = 6.98221200219

Median: ma = 20.05661711201
Median: mb = 16.62107701386
Median: mc = 7.81102496759

Inradius: r = 3.22325169332
Circumradius: R = 13.39113481445

Vertex coordinates: A[24; 0] B[0; 0] C[8.5; 6.98221200219]
Centroid: CG[10.83333333333; 2.32773733406]
Coordinates of the circumscribed circle: U[12; -5.94437534545]
Coordinates of the inscribed circle: I[9; 3.22325169332]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.7550371397° = 155°45'1″ = 0.42332358615 rad
∠ B' = β' = 140.5999431246° = 140°35'58″ = 0.68876696519 rad
∠ C' = γ' = 63.65501973562° = 63°39'1″ = 2.03106871402 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 = 11 ; ; b = 17 ; ; c = 24 ; ;

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

p = a+b+c = 11+17+24 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-11)(26-17)(26-24) } ; ; T = sqrt{ 7020 } = 83.79 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 83.79 }{ 11 } = 15.23 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 83.79 }{ 17 } = 9.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 83.79 }{ 24 } = 6.98 ; ;

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{ 11**2-17**2-24**2 }{ 2 * 17 * 24 } ) = 24° 14'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-11**2-24**2 }{ 2 * 11 * 24 } ) = 39° 24'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-11**2-17**2 }{ 2 * 17 * 11 } ) = 116° 20'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 83.79 }{ 26 } = 3.22 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 24° 14'59" } = 13.39 ; ;




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