14 25 27 triangle

Acute scalene triangle.

Sides: a = 14   b = 25   c = 27

Area: T = 173.4821987538
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 30.93220199068° = 30°55'55″ = 0.54398655917 rad
Angle ∠ B = β = 66.62201318843° = 66°37'12″ = 1.16327406495 rad
Angle ∠ C = γ = 82.44878482089° = 82°26'52″ = 1.43989864124 rad

Height: ha = 24.78331410768
Height: hb = 13.8798559003
Height: hc = 12.85105175954

Median: ma = 25.06599281723
Median: mb = 17.5
Median: mc = 15.10879449297

Inradius: r = 5.25770299254
Circumradius: R = 13.61881285074

Vertex coordinates: A[27; 0] B[0; 0] C[5.55655555556; 12.85105175954]
Centroid: CG[10.85218518519; 4.28435058651]
Coordinates of the circumscribed circle: U[13.5; 1.79898111753]
Coordinates of the inscribed circle: I[8; 5.25770299254]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.0687980093° = 149°4'5″ = 0.54398655917 rad
∠ B' = β' = 113.3879868116° = 113°22'48″ = 1.16327406495 rad
∠ C' = γ' = 97.55221517911° = 97°33'8″ = 1.43989864124 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 = 14 ; ; b = 25 ; ; c = 27 ; ;

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

p = a+b+c = 14+25+27 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-14)(33-25)(33-27) } ; ; T = sqrt{ 30096 } = 173.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 173.48 }{ 14 } = 24.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 173.48 }{ 25 } = 13.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 173.48 }{ 27 } = 12.85 ; ;

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{ 14**2-25**2-27**2 }{ 2 * 25 * 27 } ) = 30° 55'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-14**2-27**2 }{ 2 * 14 * 27 } ) = 66° 37'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-14**2-25**2 }{ 2 * 25 * 14 } ) = 82° 26'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 173.48 }{ 33 } = 5.26 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 30° 55'55" } = 13.62 ; ;




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