22 23 28 triangle

Acute scalene triangle.

Sides: a = 22   b = 23   c = 28

Area: T = 246.4377492075
Perimeter: p = 73
Semiperimeter: s = 36.5

Angle ∠ A = α = 49.9376699829° = 49°56'12″ = 0.87215598296 rad
Angle ∠ B = β = 53.14217280483° = 53°8'30″ = 0.92774981246 rad
Angle ∠ C = γ = 76.92215721227° = 76°55'18″ = 1.34325346994 rad

Height: ha = 22.40334083704
Height: hb = 21.42993471369
Height: hc = 17.60326780053

Median: ma = 23.14108729308
Median: mb = 22.43997767846
Median: mc = 17.62110101867

Inradius: r = 6.75217121116
Circumradius: R = 14.37328130415

Vertex coordinates: A[28; 0] B[0; 0] C[13.19664285714; 17.60326780053]
Centroid: CG[13.73221428571; 5.86875593351]
Coordinates of the circumscribed circle: U[14; 3.25223460341]
Coordinates of the inscribed circle: I[13.5; 6.75217121116]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.0633300171° = 130°3'48″ = 0.87215598296 rad
∠ B' = β' = 126.8588271952° = 126°51'30″ = 0.92774981246 rad
∠ C' = γ' = 103.0788427877° = 103°4'42″ = 1.34325346994 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 = 23 ; ; c = 28 ; ;

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

p = a+b+c = 22+23+28 = 73 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 73 }{ 2 } = 36.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36.5 * (36.5-22)(36.5-23)(36.5-28) } ; ; T = sqrt{ 60731.44 } = 246.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 246.44 }{ 22 } = 22.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 246.44 }{ 23 } = 21.43 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 246.44 }{ 28 } = 17.6 ; ;

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**2-23**2-28**2 }{ 2 * 23 * 28 } ) = 49° 56'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-22**2-28**2 }{ 2 * 22 * 28 } ) = 53° 8'30" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-22**2-23**2 }{ 2 * 23 * 22 } ) = 76° 55'18" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 246.44 }{ 36.5 } = 6.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 49° 56'12" } = 14.37 ; ;




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