18 22 27 triangle

Acute scalene triangle.

Sides: a = 18   b = 22   c = 27

Area: T = 197.0132531327
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 41.55552425328° = 41°33'19″ = 0.72552758037 rad
Angle ∠ B = β = 54.16993866083° = 54°10'10″ = 0.94554341501 rad
Angle ∠ C = γ = 84.27553708589° = 84°16'31″ = 1.47108826998 rad

Height: ha = 21.89902812586
Height: hb = 17.91102301207
Height: hc = 14.59435208391

Median: ma = 22.92437867727
Median: mb = 20.13770305656
Median: mc = 14.89112726118

Inradius: r = 5.88109710844
Circumradius: R = 13.56876648688

Vertex coordinates: A[27; 0] B[0; 0] C[10.5377037037; 14.59435208391]
Centroid: CG[12.5122345679; 4.86545069464]
Coordinates of the circumscribed circle: U[13.5; 1.35333403089]
Coordinates of the inscribed circle: I[11.5; 5.88109710844]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.4454757467° = 138°26'41″ = 0.72552758037 rad
∠ B' = β' = 125.8310613392° = 125°49'50″ = 0.94554341501 rad
∠ C' = γ' = 95.72546291411° = 95°43'29″ = 1.47108826998 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 = 18 ; ; b = 22 ; ; c = 27 ; ;

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

p = a+b+c = 18+22+27 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-18)(33.5-22)(33.5-27) } ; ; T = sqrt{ 38813.94 } = 197.01 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 197.01 }{ 18 } = 21.89 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 197.01 }{ 22 } = 17.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 197.01 }{ 27 } = 14.59 ; ;

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{ 18**2-22**2-27**2 }{ 2 * 22 * 27 } ) = 41° 33'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-18**2-27**2 }{ 2 * 18 * 27 } ) = 54° 10'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-18**2-22**2 }{ 2 * 22 * 18 } ) = 84° 16'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 197.01 }{ 33.5 } = 5.88 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 41° 33'19" } = 13.57 ; ;




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