6 14 16 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 14   c = 16

Area: T = 41.56992193817
Perimeter: p = 36
Semiperimeter: s = 18

Angle ∠ A = α = 21.78767892983° = 21°47'12″ = 0.38802512067 rad
Angle ∠ B = β = 60° = 1.04771975512 rad
Angle ∠ C = γ = 98.21332107017° = 98°12'48″ = 1.71441438957 rad

Height: ha = 13.85664064606
Height: hb = 5.93884599117
Height: hc = 5.19661524227

Median: ma = 14.73109198627
Median: mb = 9.84988578018
Median: mc = 7.21111025509

Inradius: r = 2.30994010768
Circumradius: R = 8.08329037687

Vertex coordinates: A[16; 0] B[0; 0] C[3; 5.19661524227]
Centroid: CG[6.33333333333; 1.73220508076]
Coordinates of the circumscribed circle: U[8; -1.15547005384]
Coordinates of the inscribed circle: I[4; 2.30994010768]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.2133210702° = 158°12'48″ = 0.38802512067 rad
∠ B' = β' = 120° = 1.04771975512 rad
∠ C' = γ' = 81.78767892983° = 81°47'12″ = 1.71441438957 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 = 16 ; ;

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

p = a+b+c = 6+14+16 = 36 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 36 }{ 2 } = 18 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18 * (18-6)(18-14)(18-16) } ; ; T = sqrt{ 1728 } = 41.57 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 41.57 }{ 6 } = 13.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 41.57 }{ 14 } = 5.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 41.57 }{ 16 } = 5.2 ; ;

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**2-16**2 }{ 2 * 14 * 16 } ) = 21° 47'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-6**2-16**2 }{ 2 * 6 * 16 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-6**2-14**2 }{ 2 * 14 * 6 } ) = 98° 12'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 41.57 }{ 18 } = 2.31 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 21° 47'12" } = 8.08 ; ;




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