19 25 27 triangle

Acute scalene triangle.

Sides: a = 19   b = 25   c = 27

Area: T = 228.6444237846
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 42.64658193109° = 42°38'45″ = 0.74443099592 rad
Angle ∠ B = β = 63.05497687879° = 63°2'59″ = 1.1100426058 rad
Angle ∠ C = γ = 74.30444119012° = 74°18'16″ = 1.29768566364 rad

Height: ha = 24.06878145101
Height: hb = 18.29215390276
Height: hc = 16.93766102108

Median: ma = 24.22329230276
Median: mb = 19.71767441531
Median: mc = 17.62881025638

Inradius: r = 6.44106827562
Circumradius: R = 14.02328768947

Vertex coordinates: A[27; 0] B[0; 0] C[8.61111111111; 16.93766102108]
Centroid: CG[11.87703703704; 5.64655367369]
Coordinates of the circumscribed circle: U[13.5; 3.79435572231]
Coordinates of the inscribed circle: I[10.5; 6.44106827562]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.3544180689° = 137°21'15″ = 0.74443099592 rad
∠ B' = β' = 116.9550231212° = 116°57'1″ = 1.1100426058 rad
∠ C' = γ' = 105.6965588099° = 105°41'44″ = 1.29768566364 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 = 19 ; ; b = 25 ; ; c = 27 ; ;

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

p = a+b+c = 19+25+27 = 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 * (35.5-19)(35.5-25)(35.5-27) } ; ; T = sqrt{ 52278.19 } = 228.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 228.64 }{ 19 } = 24.07 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 228.64 }{ 25 } = 18.29 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 228.64 }{ 27 } = 16.94 ; ;

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{ 19**2-25**2-27**2 }{ 2 * 25 * 27 } ) = 42° 38'45" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-19**2-27**2 }{ 2 * 19 * 27 } ) = 63° 2'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-19**2-25**2 }{ 2 * 25 * 19 } ) = 74° 18'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 228.64 }{ 35.5 } = 6.44 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 42° 38'45" } = 14.02 ; ;




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