16 19 24 triangle

Acute scalene triangle.

Sides: a = 16   b = 19   c = 24

Area: T = 151.6544005882
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 41.69437686839° = 41°41'38″ = 0.72876935411 rad
Angle ∠ B = β = 52.17328612599° = 52°10'22″ = 0.91105882092 rad
Angle ∠ C = γ = 86.13333700562° = 86°8' = 1.50333109033 rad

Height: ha = 18.95767507352
Height: hb = 15.96435795665
Height: hc = 12.63878338235

Median: ma = 20.11221853611
Median: mb = 18.04985456478
Median: mc = 12.82657553384

Inradius: r = 5.14108137587
Circumradius: R = 12.02773776442

Vertex coordinates: A[24; 0] B[0; 0] C[9.81325; 12.63878338235]
Centroid: CG[11.27108333333; 4.21326112745]
Coordinates of the circumscribed circle: U[12; 0.81110567161]
Coordinates of the inscribed circle: I[10.5; 5.14108137587]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.3066231316° = 138°18'22″ = 0.72876935411 rad
∠ B' = β' = 127.827713874° = 127°49'38″ = 0.91105882092 rad
∠ C' = γ' = 93.86766299438° = 93°52' = 1.50333109033 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 = 19 ; ; c = 24 ; ;

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

p = a+b+c = 16+19+24 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-16)(29.5-19)(29.5-24) } ; ; T = sqrt{ 22998.94 } = 151.65 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 151.65 }{ 16 } = 18.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 151.65 }{ 19 } = 15.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 151.65 }{ 24 } = 12.64 ; ;

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**2-19**2-24**2 }{ 2 * 19 * 24 } ) = 41° 41'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-16**2-24**2 }{ 2 * 16 * 24 } ) = 52° 10'22" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-16**2-19**2 }{ 2 * 19 * 16 } ) = 86° 8' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 151.65 }{ 29.5 } = 5.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 41° 41'38" } = 12.03 ; ;




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