13 26 28 triangle

Acute scalene triangle.

Sides: a = 13   b = 26   c = 28

Area: T = 168.3110538886
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 27.54215404525° = 27°32'30″ = 0.4810690562 rad
Angle ∠ B = β = 67.63656831745° = 67°38'8″ = 1.18804653632 rad
Angle ∠ C = γ = 84.82327763731° = 84°49'22″ = 1.48804367284 rad

Height: ha = 25.89439290593
Height: hb = 12.94769645297
Height: hc = 12.0222181349

Median: ma = 26.22549880839
Median: mb = 17.53656779168
Median: mc = 15.05499169433

Inradius: r = 5.02441951906
Circumradius: R = 14.05773490862

Vertex coordinates: A[28; 0] B[0; 0] C[4.94664285714; 12.0222181349]
Centroid: CG[10.98221428571; 4.0077393783]
Coordinates of the circumscribed circle: U[14; 1.2688488601]
Coordinates of the inscribed circle: I[7.5; 5.02441951906]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.4588459548° = 152°27'30″ = 0.4810690562 rad
∠ B' = β' = 112.3644316826° = 112°21'52″ = 1.18804653632 rad
∠ C' = γ' = 95.17772236269° = 95°10'38″ = 1.48804367284 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 = 13 ; ; b = 26 ; ; c = 28 ; ;

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

p = a+b+c = 13+26+28 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-13)(33.5-26)(33.5-28) } ; ; T = sqrt{ 28328.44 } = 168.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 168.31 }{ 13 } = 25.89 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 168.31 }{ 26 } = 12.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 168.31 }{ 28 } = 12.02 ; ;

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{ 13**2-26**2-28**2 }{ 2 * 26 * 28 } ) = 27° 32'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-13**2-28**2 }{ 2 * 13 * 28 } ) = 67° 38'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-13**2-26**2 }{ 2 * 26 * 13 } ) = 84° 49'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 168.31 }{ 33.5 } = 5.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 27° 32'30" } = 14.06 ; ;




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