22 25 28 triangle

Acute scalene triangle.

Sides: a = 22   b = 25   c = 28

Area: T = 262.7233119462
Perimeter: p = 75
Semiperimeter: s = 37.5

Angle ∠ A = α = 48.64656289465° = 48°38'44″ = 0.84990263918 rad
Angle ∠ B = β = 58.53991669546° = 58°32'21″ = 1.02217012047 rad
Angle ∠ C = γ = 72.81552040989° = 72°48'55″ = 1.2710865057 rad

Height: ha = 23.88439199511
Height: hb = 21.0187849557
Height: hc = 18.76659371044

Median: ma = 24.15657446584
Median: mb = 21.85774929944
Median: mc = 18.93440962288

Inradius: r = 7.00659498523
Circumradius: R = 14.65442108966

Vertex coordinates: A[28; 0] B[0; 0] C[11.48221428571; 18.76659371044]
Centroid: CG[13.16107142857; 6.25553123681]
Coordinates of the circumscribed circle: U[14; 4.33296532194]
Coordinates of the inscribed circle: I[12.5; 7.00659498523]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.3544371054° = 131°21'16″ = 0.84990263918 rad
∠ B' = β' = 121.4610833045° = 121°27'39″ = 1.02217012047 rad
∠ C' = γ' = 107.1854795901° = 107°11'5″ = 1.2710865057 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 = 25 ; ; c = 28 ; ;

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

p = a+b+c = 22+25+28 = 75 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 75 }{ 2 } = 37.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37.5 * (37.5-22)(37.5-25)(37.5-28) } ; ; T = sqrt{ 69023.44 } = 262.72 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 262.72 }{ 22 } = 23.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 262.72 }{ 25 } = 21.02 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 262.72 }{ 28 } = 18.77 ; ;

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**2-25**2-28**2 }{ 2 * 25 * 28 } ) = 48° 38'44" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-22**2-28**2 }{ 2 * 22 * 28 } ) = 58° 32'21" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-22**2-25**2 }{ 2 * 25 * 22 } ) = 72° 48'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 262.72 }{ 37.5 } = 7.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 48° 38'44" } = 14.65 ; ;




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