11 14 24 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 14   c = 24

Area: T = 41.67105831493
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 14.36215115629° = 14°21'41″ = 0.25106556623 rad
Angle ∠ B = β = 18.40222461959° = 18°24'8″ = 0.32111797859 rad
Angle ∠ C = γ = 147.2366242241° = 147°14'10″ = 2.57697572054 rad

Height: ha = 7.57664696635
Height: hb = 5.95329404499
Height: hc = 3.47325485958

Median: ma = 18.86113361139
Median: mb = 17.30660682999
Median: mc = 3.80878865529

Inradius: r = 1.70108401285
Circumradius: R = 22.17439157499

Vertex coordinates: A[24; 0] B[0; 0] C[10.43875; 3.47325485958]
Centroid: CG[11.47991666667; 1.15875161986]
Coordinates of the circumscribed circle: U[12; -18.64662473351]
Coordinates of the inscribed circle: I[10.5; 1.70108401285]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.6388488437° = 165°38'19″ = 0.25106556623 rad
∠ B' = β' = 161.5987753804° = 161°35'52″ = 0.32111797859 rad
∠ C' = γ' = 32.76437577589° = 32°45'50″ = 2.57697572054 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 = 11 ; ; b = 14 ; ; c = 24 ; ;

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

p = a+b+c = 11+14+24 = 49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49 }{ 2 } = 24.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.5 * (24.5-11)(24.5-14)(24.5-24) } ; ; T = sqrt{ 1736.44 } = 41.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 41.67 }{ 11 } = 7.58 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 41.67 }{ 14 } = 5.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 41.67 }{ 24 } = 3.47 ; ;

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{ 11**2-14**2-24**2 }{ 2 * 14 * 24 } ) = 14° 21'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-11**2-24**2 }{ 2 * 11 * 24 } ) = 18° 24'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-11**2-14**2 }{ 2 * 14 * 11 } ) = 147° 14'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 41.67 }{ 24.5 } = 1.7 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 14° 21'41" } = 22.17 ; ;




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