12 14 24 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 14   c = 24

Area: T = 59.79113037155
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 20.84986512302° = 20°50'55″ = 0.36438776086 rad
Angle ∠ B = β = 24.5333007117° = 24°31'59″ = 0.42881817496 rad
Angle ∠ C = γ = 134.6188341653° = 134°37'6″ = 2.35495332954 rad

Height: ha = 9.96552172859
Height: hb = 8.54216148165
Height: hc = 4.9832608643

Median: ma = 18.70882869339
Median: mb = 17.63551920885
Median: mc = 5.09990195136

Inradius: r = 2.39216521486
Circumradius: R = 16.85986389217

Vertex coordinates: A[24; 0] B[0; 0] C[10.91766666667; 4.9832608643]
Centroid: CG[11.63988888889; 1.66108695477]
Coordinates of the circumscribed circle: U[12; -11.84111868617]
Coordinates of the inscribed circle: I[11; 2.39216521486]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.151134877° = 159°9'5″ = 0.36438776086 rad
∠ B' = β' = 155.4676992883° = 155°28'1″ = 0.42881817496 rad
∠ C' = γ' = 45.38216583472° = 45°22'54″ = 2.35495332954 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 = 12 ; ; b = 14 ; ; c = 24 ; ;

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

p = a+b+c = 12+14+24 = 50 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 50 }{ 2 } = 25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25 * (25-12)(25-14)(25-24) } ; ; T = sqrt{ 3575 } = 59.79 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 59.79 }{ 12 } = 9.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 59.79 }{ 14 } = 8.54 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 59.79 }{ 24 } = 4.98 ; ;

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{ 12**2-14**2-24**2 }{ 2 * 14 * 24 } ) = 20° 50'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-12**2-24**2 }{ 2 * 12 * 24 } ) = 24° 31'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-12**2-14**2 }{ 2 * 14 * 12 } ) = 134° 37'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 59.79 }{ 25 } = 2.39 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 20° 50'55" } = 16.86 ; ;




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