14 19 24 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 19   c = 24

Area: T = 132.9155151506
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 35.65990876961° = 35°39'33″ = 0.62223684886 rad
Angle ∠ B = β = 52.29441992062° = 52°17'39″ = 0.91327059558 rad
Angle ∠ C = γ = 92.04767130977° = 92°2'48″ = 1.60765182092 rad

Height: ha = 18.98878787866
Height: hb = 13.99110685796
Height: hc = 11.07662626255

Median: ma = 20.48216991483
Median: mb = 17.19773835219
Median: mc = 11.59774135047

Inradius: r = 4.66436895265
Circumradius: R = 12.00876603902

Vertex coordinates: A[24; 0] B[0; 0] C[8.56325; 11.07662626255]
Centroid: CG[10.85441666667; 3.69220875418]
Coordinates of the circumscribed circle: U[12; -0.42988450139]
Coordinates of the inscribed circle: I[9.5; 4.66436895265]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.3410912304° = 144°20'27″ = 0.62223684886 rad
∠ B' = β' = 127.7065800794° = 127°42'21″ = 0.91327059558 rad
∠ C' = γ' = 87.95332869023° = 87°57'12″ = 1.60765182092 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 = 19 ; ; c = 24 ; ;

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

p = a+b+c = 14+19+24 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-14)(28.5-19)(28.5-24) } ; ; T = sqrt{ 17666.44 } = 132.92 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 132.92 }{ 14 } = 18.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 132.92 }{ 19 } = 13.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 132.92 }{ 24 } = 11.08 ; ;

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**2-19**2-24**2 }{ 2 * 19 * 24 } ) = 35° 39'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-14**2-24**2 }{ 2 * 14 * 24 } ) = 52° 17'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-14**2-19**2 }{ 2 * 19 * 14 } ) = 92° 2'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 132.92 }{ 28.5 } = 4.66 ; ;

7. Circumradius

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




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