18 25 28 triangle

Acute scalene triangle.

Sides: a = 18   b = 25   c = 28

Area: T = 221.1866431546
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 39.1954967426° = 39°11'42″ = 0.68440812318 rad
Angle ∠ B = β = 61.36990101631° = 61°22'8″ = 1.0711091286 rad
Angle ∠ C = γ = 79.43660224109° = 79°26'10″ = 1.38664201358 rad

Height: ha = 24.57662701718
Height: hb = 17.69549145237
Height: hc = 15.79990308247

Median: ma = 24.97699819784
Median: mb = 19.94436706752
Median: mc = 16.68883192683

Inradius: r = 6.23106037055
Circumradius: R = 14.24113798983

Vertex coordinates: A[28; 0] B[0; 0] C[8.625; 15.79990308247]
Centroid: CG[12.20883333333; 5.26663436082]
Coordinates of the circumscribed circle: U[14; 2.6110919648]
Coordinates of the inscribed circle: I[10.5; 6.23106037055]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.8055032574° = 140°48'18″ = 0.68440812318 rad
∠ B' = β' = 118.6310989837° = 118°37'52″ = 1.0711091286 rad
∠ C' = γ' = 100.5643977589° = 100°33'50″ = 1.38664201358 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 = 25 ; ; c = 28 ; ;

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

p = a+b+c = 18+25+28 = 71 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 71 }{ 2 } = 35.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.5 * (35.5-18)(35.5-25)(35.5-28) } ; ; T = sqrt{ 48923.44 } = 221.19 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 221.19 }{ 18 } = 24.58 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 221.19 }{ 25 } = 17.69 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 221.19 }{ 28 } = 15.8 ; ;

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**2-25**2-28**2 }{ 2 * 25 * 28 } ) = 39° 11'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-18**2-28**2 }{ 2 * 18 * 28 } ) = 61° 22'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-18**2-25**2 }{ 2 * 25 * 18 } ) = 79° 26'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 221.19 }{ 35.5 } = 6.23 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 39° 11'42" } = 14.24 ; ;




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