9 16 24 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 16   c = 24

Area: T = 40.17438409914
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 12.07877450929° = 12°4'40″ = 0.21107964181 rad
Angle ∠ B = β = 21.83877815071° = 21°50'16″ = 0.38111411886 rad
Angle ∠ C = γ = 146.08444734° = 146°5'4″ = 2.55496550469 rad

Height: ha = 8.92875202203
Height: hb = 5.02217301239
Height: hc = 3.34878200826

Median: ma = 19.89334662641
Median: mb = 16.26334559673
Median: mc = 4.95497474683

Inradius: r = 1.64397486119
Circumradius: R = 21.50765320786

Vertex coordinates: A[24; 0] B[0; 0] C[8.35441666667; 3.34878200826]
Centroid: CG[10.78547222222; 1.11659400275]
Coordinates of the circumscribed circle: U[12; -17.84774346069]
Coordinates of the inscribed circle: I[8.5; 1.64397486119]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.9222254907° = 167°55'20″ = 0.21107964181 rad
∠ B' = β' = 158.1622218493° = 158°9'44″ = 0.38111411886 rad
∠ C' = γ' = 33.91655266° = 33°54'56″ = 2.55496550469 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 = 16 ; ; c = 24 ; ;

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

p = a+b+c = 9+16+24 = 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)(24.5-16)(24.5-24) } ; ; T = sqrt{ 1613.94 } = 40.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 40.17 }{ 9 } = 8.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 40.17 }{ 16 } = 5.02 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 40.17 }{ 24 } = 3.35 ; ;

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**2-16**2-24**2 }{ 2 * 16 * 24 } ) = 12° 4'40" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-9**2-24**2 }{ 2 * 9 * 24 } ) = 21° 50'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-9**2-16**2 }{ 2 * 16 * 9 } ) = 146° 5'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 40.17 }{ 24.5 } = 1.64 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 12° 4'40" } = 21.51 ; ;




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