7 14 18 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 14   c = 18

Area: T = 44.84334777866
Perimeter: p = 39
Semiperimeter: s = 19.5

Angle ∠ A = α = 20.84986512302° = 20°50'55″ = 0.36438776086 rad
Angle ∠ B = β = 45.38216583472° = 45°22'54″ = 0.79220593582 rad
Angle ∠ C = γ = 113.7769690423° = 113°46'11″ = 1.98656556869 rad

Height: ha = 12.81224222248
Height: hb = 6.40662111124
Height: hc = 4.9832608643

Median: ma = 15.74400762387
Median: mb = 11.72660393996
Median: mc = 6.44220493634

Inradius: r = 2.32996655275
Circumradius: R = 9.83442060377

Vertex coordinates: A[18; 0] B[0; 0] C[4.91766666667; 4.9832608643]
Centroid: CG[7.63988888889; 1.66108695477]
Coordinates of the circumscribed circle: U[9; -3.96437871274]
Coordinates of the inscribed circle: I[5.5; 2.32996655275]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.151134877° = 159°9'5″ = 0.36438776086 rad
∠ B' = β' = 134.6188341653° = 134°37'6″ = 0.79220593582 rad
∠ C' = γ' = 66.23303095773° = 66°13'49″ = 1.98656556869 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 = 7 ; ; b = 14 ; ; c = 18 ; ;

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

p = a+b+c = 7+14+18 = 39 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 39 }{ 2 } = 19.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.5 * (19.5-7)(19.5-14)(19.5-18) } ; ; T = sqrt{ 2010.94 } = 44.84 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 44.84 }{ 7 } = 12.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 44.84 }{ 14 } = 6.41 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 44.84 }{ 18 } = 4.98 ; ;

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{ 7**2-14**2-18**2 }{ 2 * 14 * 18 } ) = 20° 50'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-7**2-18**2 }{ 2 * 7 * 18 } ) = 45° 22'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-7**2-14**2 }{ 2 * 14 * 7 } ) = 113° 46'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 44.84 }{ 19.5 } = 2.3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 20° 50'55" } = 9.83 ; ;




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