8 12 18 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 12   c = 18

Area: T = 38.24991829978
Perimeter: p = 38
Semiperimeter: s = 19

Angle ∠ A = α = 20.74219164807° = 20°44'31″ = 0.36220147358 rad
Angle ∠ B = β = 32.08991838633° = 32°5'21″ = 0.56600619127 rad
Angle ∠ C = γ = 127.1698899656° = 127°10'8″ = 2.22195160051 rad

Height: ha = 9.56222957495
Height: hb = 6.3754863833
Height: hc = 4.2549909222

Median: ma = 14.76548230602
Median: mb = 12.576980509
Median: mc = 4.79658315233

Inradius: r = 2.01331148946
Circumradius: R = 11.29443588893

Vertex coordinates: A[18; 0] B[0; 0] C[6.77877777778; 4.2549909222]
Centroid: CG[8.25992592593; 1.41766364073]
Coordinates of the circumscribed circle: U[9; -6.82436751623]
Coordinates of the inscribed circle: I[7; 2.01331148946]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.2588083519° = 159°15'29″ = 0.36220147358 rad
∠ B' = β' = 147.9110816137° = 147°54'39″ = 0.56600619127 rad
∠ C' = γ' = 52.8311100344° = 52°49'52″ = 2.22195160051 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 = 8 ; ; b = 12 ; ; c = 18 ; ;

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

p = a+b+c = 8+12+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 * (19-8)(19-12)(19-18) } ; ; T = sqrt{ 1463 } = 38.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 38.25 }{ 8 } = 9.56 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 38.25 }{ 12 } = 6.37 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 38.25 }{ 18 } = 4.25 ; ;

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{ 8**2-12**2-18**2 }{ 2 * 12 * 18 } ) = 20° 44'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-8**2-18**2 }{ 2 * 8 * 18 } ) = 32° 5'21" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-8**2-12**2 }{ 2 * 12 * 8 } ) = 127° 10'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 38.25 }{ 19 } = 2.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 20° 44'31" } = 11.29 ; ;




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