16 22 24 triangle

Acute scalene triangle.

Sides: a = 16   b = 22   c = 24

Area: T = 171.1587821907
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 40.41554390215° = 40°24'56″ = 0.70553824796 rad
Angle ∠ B = β = 63.05656418195° = 63°3'20″ = 1.10105285617 rad
Angle ∠ C = γ = 76.5298919159° = 76°31'44″ = 1.33656816123 rad

Height: ha = 21.39547277384
Height: hb = 15.56598019916
Height: hc = 14.26331518256

Median: ma = 21.58770331449
Median: mb = 17.17655640373
Median: mc = 15.03332963784

Inradius: r = 5.52112200615
Circumradius: R = 12.33994886454

Vertex coordinates: A[24; 0] B[0; 0] C[7.25; 14.26331518256]
Centroid: CG[10.41766666667; 4.75443839419]
Coordinates of the circumscribed circle: U[12; 2.87545399685]
Coordinates of the inscribed circle: I[9; 5.52112200615]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.5854560979° = 139°35'4″ = 0.70553824796 rad
∠ B' = β' = 116.944435818° = 116°56'40″ = 1.10105285617 rad
∠ C' = γ' = 103.4711080841° = 103°28'16″ = 1.33656816123 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 = 16 ; ; b = 22 ; ; c = 24 ; ;

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

p = a+b+c = 16+22+24 = 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 * (31-16)(31-22)(31-24) } ; ; T = sqrt{ 29295 } = 171.16 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 171.16 }{ 16 } = 21.39 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 171.16 }{ 22 } = 15.56 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 171.16 }{ 24 } = 14.26 ; ;

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{ 16**2-22**2-24**2 }{ 2 * 22 * 24 } ) = 40° 24'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-16**2-24**2 }{ 2 * 16 * 24 } ) = 63° 3'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-16**2-22**2 }{ 2 * 22 * 16 } ) = 76° 31'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 171.16 }{ 31 } = 5.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 40° 24'56" } = 12.34 ; ;




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