14 21 28 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 21   c = 28

Area: T = 142.3322137973
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 28.95550243719° = 28°57'18″ = 0.50553605103 rad
Angle ∠ B = β = 46.56774634422° = 46°34'3″ = 0.81327555614 rad
Angle ∠ C = γ = 104.4787512186° = 104°28'39″ = 1.82334765819 rad

Height: ha = 20.33331625676
Height: hb = 13.55554417117
Height: hc = 10.16765812838

Median: ma = 23.73881549409
Median: mb = 19.48771752699
Median: mc = 11.06879718106

Inradius: r = 4.51884805706
Circumradius: R = 14.45991378258

Vertex coordinates: A[28; 0] B[0; 0] C[9.625; 10.16765812838]
Centroid: CG[12.54216666667; 3.38988604279]
Coordinates of the circumscribed circle: U[14; -3.61547844565]
Coordinates of the inscribed circle: I[10.5; 4.51884805706]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.0454975628° = 151°2'42″ = 0.50553605103 rad
∠ B' = β' = 133.4332536558° = 133°25'57″ = 0.81327555614 rad
∠ C' = γ' = 75.52224878141° = 75°31'21″ = 1.82334765819 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 = 21 ; ; c = 28 ; ;

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

p = a+b+c = 14+21+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 * (31.5-14)(31.5-21)(31.5-28) } ; ; T = sqrt{ 20258.44 } = 142.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 142.33 }{ 14 } = 20.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 142.33 }{ 21 } = 13.56 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 142.33 }{ 28 } = 10.17 ; ;

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**2-21**2-28**2 }{ 2 * 21 * 28 } ) = 28° 57'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-14**2-28**2 }{ 2 * 14 * 28 } ) = 46° 34'3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-14**2-21**2 }{ 2 * 21 * 14 } ) = 104° 28'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 142.33 }{ 31.5 } = 4.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 28° 57'18" } = 14.46 ; ;




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