16 18 24 triangle

Acute scalene triangle.

Sides: a = 16   b = 18   c = 24

Area: T = 143.9976527736
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 41.80990791939° = 41°48'33″ = 0.73297060892 rad
Angle ∠ B = β = 48.58988113619° = 48°35'20″ = 0.84880347379 rad
Angle ∠ C = γ = 89.60221094442° = 89°36'8″ = 1.56438518265 rad

Height: ha = 187.999565967
Height: hb = 165.9996141929
Height: hc = 121.9997106447

Median: ma = 19.64768827044
Median: mb = 18.30330052177
Median: mc = 12.08330459736

Inradius: r = 4.96553975081
Circumradius: R = 122.0002893623

Vertex coordinates: A[24; 0] B[0; 0] C[10.58333333333; 121.9997106447]
Centroid: CG[11.52877777778; 43.9999035482]
Coordinates of the circumscribed circle: U[12; 0.08333353428]
Coordinates of the inscribed circle: I[11; 4.96553975081]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.1910920806° = 138°11'27″ = 0.73297060892 rad
∠ B' = β' = 131.4111188638° = 131°24'40″ = 0.84880347379 rad
∠ C' = γ' = 90.39878905558° = 90°23'52″ = 1.56438518265 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 = 18 ; ; c = 24 ; ;

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

p = a+b+c = 16+18+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 * (29-16)(29-18)(29-24) } ; ; T = sqrt{ 20735 } = 144 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 144 }{ 16 } = 18 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 144 }{ 18 } = 16 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 144 }{ 24 } = 12 ; ;

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**2-18**2-24**2 }{ 2 * 18 * 24 } ) = 41° 48'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-16**2-24**2 }{ 2 * 16 * 24 } ) = 48° 35'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-16**2-18**2 }{ 2 * 18 * 16 } ) = 89° 36'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 144 }{ 29 } = 4.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 41° 48'33" } = 12 ; ;




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