8 22 27 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 22   c = 27

Area: T = 75.47547474325
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 14.7221668176° = 14°43'18″ = 0.25769415811 rad
Angle ∠ B = β = 44.33440313162° = 44°20'3″ = 0.77437748172 rad
Angle ∠ C = γ = 120.9444300508° = 120°56'39″ = 2.11108762554 rad

Height: ha = 18.86986868581
Height: hb = 6.86113406757
Height: hc = 5.5910722032

Median: ma = 24.33002057604
Median: mb = 16.59881926727
Median: mc = 9.57986220303

Inradius: r = 2.6488236752
Circumradius: R = 15.74403640345

Vertex coordinates: A[27; 0] B[0; 0] C[5.72222222222; 5.5910722032]
Centroid: CG[10.90774074074; 1.86435740107]
Coordinates of the circumscribed circle: U[13.5; -8.09437667337]
Coordinates of the inscribed circle: I[6.5; 2.6488236752]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.2788331824° = 165°16'42″ = 0.25769415811 rad
∠ B' = β' = 135.6665968684° = 135°39'57″ = 0.77437748172 rad
∠ C' = γ' = 59.05656994922° = 59°3'21″ = 2.11108762554 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 = 22 ; ; c = 27 ; ;

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

p = a+b+c = 8+22+27 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-8)(28.5-22)(28.5-27) } ; ; T = sqrt{ 5696.44 } = 75.47 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 75.47 }{ 8 } = 18.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 75.47 }{ 22 } = 6.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 75.47 }{ 27 } = 5.59 ; ;

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{ 8**2-22**2-27**2 }{ 2 * 22 * 27 } ) = 14° 43'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-8**2-27**2 }{ 2 * 8 * 27 } ) = 44° 20'3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-8**2-22**2 }{ 2 * 22 * 8 } ) = 120° 56'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 75.47 }{ 28.5 } = 2.65 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 14° 43'18" } = 15.74 ; ;




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