10 16 24 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 16   c = 24

Area: T = 58.09547501931
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 17.61224390704° = 17°36'45″ = 0.30773950511 rad
Angle ∠ B = β = 28.95550243719° = 28°57'18″ = 0.50553605103 rad
Angle ∠ C = γ = 133.4332536558° = 133°25'57″ = 2.32988370922 rad

Height: ha = 11.61989500386
Height: hb = 7.26218437741
Height: hc = 4.84112291828

Median: ma = 19.77437199333
Median: mb = 16.55329453572
Median: mc = 5.83109518948

Inradius: r = 2.32437900077
Circumradius: R = 16.52547289438

Vertex coordinates: A[24; 0] B[0; 0] C[8.75; 4.84112291828]
Centroid: CG[10.91766666667; 1.61437430609]
Coordinates of the circumscribed circle: U[12; -11.36107511489]
Coordinates of the inscribed circle: I[9; 2.32437900077]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.388756093° = 162°23'15″ = 0.30773950511 rad
∠ B' = β' = 151.0454975628° = 151°2'42″ = 0.50553605103 rad
∠ C' = γ' = 46.56774634422° = 46°34'3″ = 2.32988370922 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 = 10 ; ; b = 16 ; ; c = 24 ; ;

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

p = a+b+c = 10+16+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 * (25-10)(25-16)(25-24) } ; ; T = sqrt{ 3375 } = 58.09 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 58.09 }{ 10 } = 11.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 58.09 }{ 16 } = 7.26 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 58.09 }{ 24 } = 4.84 ; ;

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{ 10**2-16**2-24**2 }{ 2 * 16 * 24 } ) = 17° 36'45" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-10**2-24**2 }{ 2 * 10 * 24 } ) = 28° 57'18" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-10**2-16**2 }{ 2 * 16 * 10 } ) = 133° 25'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 58.09 }{ 25 } = 2.32 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 17° 36'45" } = 16.52 ; ;




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