14 16 24 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 16   c = 24

Area: T = 107.6244346688
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 34.09333908114° = 34°5'36″ = 0.59550419228 rad
Angle ∠ B = β = 39.83881498056° = 39°50'17″ = 0.6955306882 rad
Angle ∠ C = γ = 106.0688459383° = 106°4'6″ = 1.85112438488 rad

Height: ha = 15.37549066697
Height: hb = 13.4533043336
Height: hc = 8.96986955573

Median: ma = 19.15772440607
Median: mb = 17.94443584449
Median: mc = 9.05553851381

Inradius: r = 3.98660869144
Circumradius: R = 12.48878806828

Vertex coordinates: A[24; 0] B[0; 0] C[10.75; 8.96986955573]
Centroid: CG[11.58333333333; 2.99895651858]
Coordinates of the circumscribed circle: U[12; -3.45664669747]
Coordinates of the inscribed circle: I[11; 3.98660869144]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.9076609189° = 145°54'24″ = 0.59550419228 rad
∠ B' = β' = 140.1621850194° = 140°9'43″ = 0.6955306882 rad
∠ C' = γ' = 73.9321540617° = 73°55'54″ = 1.85112438488 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 = 16 ; ; c = 24 ; ;

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

p = a+b+c = 14+16+24 = 54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54 }{ 2 } = 27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27 * (27-14)(27-16)(27-24) } ; ; T = sqrt{ 11583 } = 107.62 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 107.62 }{ 14 } = 15.37 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 107.62 }{ 16 } = 13.45 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 107.62 }{ 24 } = 8.97 ; ;

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**2-16**2-24**2 }{ 2 * 16 * 24 } ) = 34° 5'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-14**2-24**2 }{ 2 * 14 * 24 } ) = 39° 50'17" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-14**2-16**2 }{ 2 * 16 * 14 } ) = 106° 4'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 107.62 }{ 27 } = 3.99 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 34° 5'36" } = 12.49 ; ;




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