16 27 28 triangle

Acute scalene triangle.

Sides: a = 16   b = 27   c = 28

Area: T = 210.07436478
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 33.76224154142° = 33°45'45″ = 0.58992653124 rad
Angle ∠ B = β = 69.69900687004° = 69°41'24″ = 1.21663211548 rad
Angle ∠ C = γ = 76.54875158854° = 76°32'51″ = 1.33660061864 rad

Height: ha = 26.2599205975
Height: hb = 15.56110109481
Height: hc = 15.00552605571

Median: ma = 26.31553947339
Median: mb = 18.37879759495
Median: mc = 17.21991753577

Inradius: r = 5.91875675437
Circumradius: R = 14.39549516356

Vertex coordinates: A[28; 0] B[0; 0] C[5.55435714286; 15.00552605571]
Centroid: CG[11.18545238095; 5.0021753519]
Coordinates of the circumscribed circle: U[14; 3.34988255541]
Coordinates of the inscribed circle: I[8.5; 5.91875675437]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.2387584586° = 146°14'15″ = 0.58992653124 rad
∠ B' = β' = 110.31099313° = 110°18'36″ = 1.21663211548 rad
∠ C' = γ' = 103.4522484115° = 103°27'9″ = 1.33660061864 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 = 16 ; ; b = 27 ; ; c = 28 ; ;

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

p = a+b+c = 16+27+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 * (35.5-16)(35.5-27)(35.5-28) } ; ; T = sqrt{ 44130.94 } = 210.07 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 210.07 }{ 16 } = 26.26 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 210.07 }{ 27 } = 15.56 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 210.07 }{ 28 } = 15.01 ; ;

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{ 16**2-27**2-28**2 }{ 2 * 27 * 28 } ) = 33° 45'45" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-16**2-28**2 }{ 2 * 16 * 28 } ) = 69° 41'24" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-16**2-27**2 }{ 2 * 27 * 16 } ) = 76° 32'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 210.07 }{ 35.5 } = 5.92 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 33° 45'45" } = 14.39 ; ;




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