11 24 28 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 24   c = 28

Area: T = 130.196576606
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 22.79882480997° = 22°47'54″ = 0.3987904493 rad
Angle ∠ B = β = 57.71877199078° = 57°43'4″ = 1.00773642491 rad
Angle ∠ C = γ = 99.48440319925° = 99°29'3″ = 1.73663239114 rad

Height: ha = 23.67219574655
Height: hb = 10.85496471717
Height: hc = 9.32996975757

Median: ma = 25.49901941931
Median: mb = 17.56441680703
Median: mc = 12.34990890352

Inradius: r = 4.13331989225
Circumradius: R = 14.19440099584

Vertex coordinates: A[28; 0] B[0; 0] C[5.875; 9.32996975757]
Centroid: CG[11.29216666667; 3.10998991919]
Coordinates of the circumscribed circle: U[14; -2.33987857318]
Coordinates of the inscribed circle: I[7.5; 4.13331989225]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.20217519° = 157°12'6″ = 0.3987904493 rad
∠ B' = β' = 122.2822280092° = 122°16'56″ = 1.00773642491 rad
∠ C' = γ' = 80.51659680075° = 80°30'57″ = 1.73663239114 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 = 24 ; ; c = 28 ; ;

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

p = a+b+c = 11+24+28 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-11)(31.5-24)(31.5-28) } ; ; T = sqrt{ 16950.94 } = 130.2 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 130.2 }{ 11 } = 23.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 130.2 }{ 24 } = 10.85 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 130.2 }{ 28 } = 9.3 ; ;

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**2-24**2-28**2 }{ 2 * 24 * 28 } ) = 22° 47'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-11**2-28**2 }{ 2 * 11 * 28 } ) = 57° 43'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-11**2-24**2 }{ 2 * 24 * 11 } ) = 99° 29'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 130.2 }{ 31.5 } = 4.13 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 22° 47'54" } = 14.19 ; ;




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