5 14 18 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 14   c = 18

Area: T = 23.70552209439
Perimeter: p = 37
Semiperimeter: s = 18.5

Angle ∠ A = α = 10.84440625637° = 10°50'39″ = 0.1899264596 rad
Angle ∠ B = β = 31.78883306171° = 31°47'18″ = 0.5554811033 rad
Angle ∠ C = γ = 137.3687606819° = 137°22'3″ = 2.39875170246 rad

Height: ha = 9.48220883776
Height: hb = 3.38664601348
Height: hc = 2.63439134382

Median: ma = 15.93295323221
Median: mb = 11.20326782512
Median: mc = 5.43113902456

Inradius: r = 1.28113632943
Circumradius: R = 13.28882119405

Vertex coordinates: A[18; 0] B[0; 0] C[4.25; 2.63439134382]
Centroid: CG[7.41766666667; 0.87879711461]
Coordinates of the circumscribed circle: U[9; -9.77663273563]
Coordinates of the inscribed circle: I[4.5; 1.28113632943]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.1565937436° = 169°9'21″ = 0.1899264596 rad
∠ B' = β' = 148.2121669383° = 148°12'42″ = 0.5554811033 rad
∠ C' = γ' = 42.63223931807° = 42°37'57″ = 2.39875170246 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 = 5 ; ; b = 14 ; ; c = 18 ; ;

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

p = a+b+c = 5+14+18 = 37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 37 }{ 2 } = 18.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.5 * (18.5-5)(18.5-14)(18.5-18) } ; ; T = sqrt{ 561.94 } = 23.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 23.71 }{ 5 } = 9.48 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 23.71 }{ 14 } = 3.39 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 23.71 }{ 18 } = 2.63 ; ;

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{ 5**2-14**2-18**2 }{ 2 * 14 * 18 } ) = 10° 50'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-5**2-18**2 }{ 2 * 5 * 18 } ) = 31° 47'18" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-5**2-14**2 }{ 2 * 14 * 5 } ) = 137° 22'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 23.71 }{ 18.5 } = 1.28 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 10° 50'39" } = 13.29 ; ;




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