14 20 24 triangle

Acute scalene triangle.

Sides: a = 14   b = 20   c = 24

Area: T = 139.9110685796
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 35.65990876961° = 35°39'33″ = 0.62223684886 rad
Angle ∠ B = β = 56.38876254015° = 56°23'15″ = 0.98441497206 rad
Angle ∠ C = γ = 87.95332869023° = 87°57'12″ = 1.53550744444 rad

Height: ha = 19.9877240828
Height: hb = 13.99110685796
Height: hc = 11.65992238164

Median: ma = 20.95223268398
Median: mb = 16.91215345253
Median: mc = 12.4109673646

Inradius: r = 4.82545064068
Circumradius: R = 12.00876603902

Vertex coordinates: A[24; 0] B[0; 0] C[7.75; 11.65992238164]
Centroid: CG[10.58333333333; 3.88664079388]
Coordinates of the circumscribed circle: U[12; 0.42988450139]
Coordinates of the inscribed circle: I[9; 4.82545064068]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.3410912304° = 144°20'27″ = 0.62223684886 rad
∠ B' = β' = 123.6122374598° = 123°36'45″ = 0.98441497206 rad
∠ C' = γ' = 92.04767130977° = 92°2'48″ = 1.53550744444 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 = 14 ; ; b = 20 ; ; c = 24 ; ;

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

p = a+b+c = 14+20+24 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-14)(29-20)(29-24) } ; ; T = sqrt{ 19575 } = 139.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 139.91 }{ 14 } = 19.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 139.91 }{ 20 } = 13.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 139.91 }{ 24 } = 11.66 ; ;

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{ 14**2-20**2-24**2 }{ 2 * 20 * 24 } ) = 35° 39'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-14**2-24**2 }{ 2 * 14 * 24 } ) = 56° 23'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-14**2-20**2 }{ 2 * 20 * 14 } ) = 87° 57'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 139.91 }{ 29 } = 4.82 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 35° 39'33" } = 12.01 ; ;




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