18 20 28 triangle

Obtuse scalene triangle.

Sides: a = 18   b = 20   c = 28

Area: T = 179.3743911147
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 39.83881498056° = 39°50'17″ = 0.6955306882 rad
Angle ∠ B = β = 45.38216583472° = 45°22'54″ = 0.79220593582 rad
Angle ∠ C = γ = 94.78801918472° = 94°46'49″ = 1.65442264134 rad

Height: ha = 19.93304345718
Height: hb = 17.93773911147
Height: hc = 12.81224222248

Median: ma = 22.60553091109
Median: mb = 21.30772757527
Median: mc = 12.88440987267

Inradius: r = 5.4365573065
Circumradius: R = 14.04988657681

Vertex coordinates: A[28; 0] B[0; 0] C[12.64328571429; 12.81224222248]
Centroid: CG[13.54876190476; 4.27108074083]
Coordinates of the circumscribed circle: U[14; -1.1710738814]
Coordinates of the inscribed circle: I[13; 5.4365573065]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.1621850194° = 140°9'43″ = 0.6955306882 rad
∠ B' = β' = 134.6188341653° = 134°37'6″ = 0.79220593582 rad
∠ C' = γ' = 85.22198081528° = 85°13'11″ = 1.65442264134 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 = 18 ; ; b = 20 ; ; c = 28 ; ;

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

p = a+b+c = 18+20+28 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-18)(33-20)(33-28) } ; ; T = sqrt{ 32175 } = 179.37 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 179.37 }{ 18 } = 19.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 179.37 }{ 20 } = 17.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 179.37 }{ 28 } = 12.81 ; ;

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{ 18**2-20**2-28**2 }{ 2 * 20 * 28 } ) = 39° 50'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-18**2-28**2 }{ 2 * 18 * 28 } ) = 45° 22'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-18**2-20**2 }{ 2 * 20 * 18 } ) = 94° 46'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 179.37 }{ 33 } = 5.44 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 39° 50'17" } = 14.05 ; ;




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