22 27 28 triangle

Acute scalene triangle.

Sides: a = 22   b = 27   c = 28

Area: T = 276.9599270471
Perimeter: p = 77
Semiperimeter: s = 38.5

Angle ∠ A = α = 47.11329286182° = 47°6'47″ = 0.82222757246 rad
Angle ∠ B = β = 64.05655202276° = 64°3'20″ = 1.1187979732 rad
Angle ∠ C = γ = 68.83215511542° = 68°49'54″ = 1.20113371969 rad

Height: ha = 25.17881154974
Height: hb = 20.51655015164
Height: hc = 19.78328050337

Median: ma = 25.20991253319
Median: mb = 21.25444113068
Median: mc = 20.26107995894

Inradius: r = 7.1943747285
Circumradius: R = 15.01330378121

Vertex coordinates: A[28; 0] B[0; 0] C[9.625; 19.78328050337]
Centroid: CG[12.54216666667; 6.59442683446]
Coordinates of the circumscribed circle: U[14; 5.42113747655]
Coordinates of the inscribed circle: I[11.5; 7.1943747285]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.8877071382° = 132°53'13″ = 0.82222757246 rad
∠ B' = β' = 115.9444479772° = 115°56'40″ = 1.1187979732 rad
∠ C' = γ' = 111.1688448846° = 111°10'6″ = 1.20113371969 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 = 22 ; ; b = 27 ; ; c = 28 ; ;

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

p = a+b+c = 22+27+28 = 77 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 77 }{ 2 } = 38.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38.5 * (38.5-22)(38.5-27)(38.5-28) } ; ; T = sqrt{ 76706.44 } = 276.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 276.96 }{ 22 } = 25.18 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 276.96 }{ 27 } = 20.52 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 276.96 }{ 28 } = 19.78 ; ;

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{ 22**2-27**2-28**2 }{ 2 * 27 * 28 } ) = 47° 6'47" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-22**2-28**2 }{ 2 * 22 * 28 } ) = 64° 3'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-22**2-27**2 }{ 2 * 27 * 22 } ) = 68° 49'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 276.96 }{ 38.5 } = 7.19 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 47° 6'47" } = 15.01 ; ;




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