14 15 28 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 15   c = 28

Area: T = 52.81551256744
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 14.56663276483° = 14°33'59″ = 0.25442303774 rad
Angle ∠ B = β = 15.63224293747° = 15°37'57″ = 0.27328373627 rad
Angle ∠ C = γ = 149.8011242977° = 149°48'4″ = 2.61545249135 rad

Height: ha = 7.54550179535
Height: hb = 7.04220167566
Height: hc = 3.77325089767

Median: ma = 21.34224459704
Median: mb = 20.82766655997
Median: mc = 3.80878865529

Inradius: r = 1.85331623044
Circumradius: R = 27.8332935759

Vertex coordinates: A[28; 0] B[0; 0] C[13.48221428571; 3.77325089767]
Centroid: CG[13.82773809524; 1.25875029922]
Coordinates of the circumscribed circle: U[14; -24.05656087632]
Coordinates of the inscribed circle: I[13.5; 1.85331623044]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.4343672352° = 165°26'1″ = 0.25442303774 rad
∠ B' = β' = 164.3687570625° = 164°22'3″ = 0.27328373627 rad
∠ C' = γ' = 30.1998757023° = 30°11'56″ = 2.61545249135 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 = 15 ; ; c = 28 ; ;

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

p = a+b+c = 14+15+28 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-14)(28.5-15)(28.5-28) } ; ; T = sqrt{ 2789.44 } = 52.82 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 52.82 }{ 14 } = 7.55 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 52.82 }{ 15 } = 7.04 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 52.82 }{ 28 } = 3.77 ; ;

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**2-15**2-28**2 }{ 2 * 15 * 28 } ) = 14° 33'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-14**2-28**2 }{ 2 * 14 * 28 } ) = 15° 37'57" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-14**2-15**2 }{ 2 * 15 * 14 } ) = 149° 48'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 52.82 }{ 28.5 } = 1.85 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 14° 33'59" } = 27.83 ; ;




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