6 14 18 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 14   c = 18

Area: T = 35.14325667816
Perimeter: p = 38
Semiperimeter: s = 19

Angle ∠ A = α = 16.1955116739° = 16°11'42″ = 0.28326581098 rad
Angle ∠ B = β = 40.60110607311° = 40°36'4″ = 0.70986221896 rad
Angle ∠ C = γ = 123.204382253° = 123°12'14″ = 2.15503123542 rad

Height: ha = 11.71441889272
Height: hb = 5.02203666831
Height: hc = 3.90547296424

Median: ma = 15.84329795178
Median: mb = 11.44655231423
Median: mc = 5.91660797831

Inradius: r = 1.8549608778
Circumradius: R = 10.75661864319

Vertex coordinates: A[18; 0] B[0; 0] C[4.55655555556; 3.90547296424]
Centroid: CG[7.51985185185; 1.30215765475]
Coordinates of the circumscribed circle: U[9; -5.89902925699]
Coordinates of the inscribed circle: I[5; 1.8549608778]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.8054883261° = 163°48'18″ = 0.28326581098 rad
∠ B' = β' = 139.3998939269° = 139°23'56″ = 0.70986221896 rad
∠ C' = γ' = 56.796617747° = 56°47'46″ = 2.15503123542 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 = 6 ; ; b = 14 ; ; c = 18 ; ;

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

p = a+b+c = 6+14+18 = 38 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 38 }{ 2 } = 19 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19 * (19-6)(19-14)(19-18) } ; ; T = sqrt{ 1235 } = 35.14 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 35.14 }{ 6 } = 11.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 35.14 }{ 14 } = 5.02 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 35.14 }{ 18 } = 3.9 ; ;

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{ 6**2-14**2-18**2 }{ 2 * 14 * 18 } ) = 16° 11'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-6**2-18**2 }{ 2 * 6 * 18 } ) = 40° 36'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-6**2-14**2 }{ 2 * 14 * 6 } ) = 123° 12'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 35.14 }{ 19 } = 1.85 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 16° 11'42" } = 10.76 ; ;




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