14 27 28 triangle

Acute scalene triangle.

Sides: a = 14   b = 27   c = 28

Area: T = 185.6843702839
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 29.42112427193° = 29°25'16″ = 0.51334975555 rad
Angle ∠ B = β = 71.32878183712° = 71°19'40″ = 1.24549052788 rad
Angle ∠ C = γ = 79.25109389095° = 79°15'3″ = 1.38331898193 rad

Height: ha = 26.52662432627
Height: hb = 13.75443483584
Height: hc = 13.26331216314

Median: ma = 26.59988721565
Median: mb = 17.54328047928
Median: mc = 16.32548277173

Inradius: r = 5.38221363142
Circumradius: R = 14.25500389617

Vertex coordinates: A[28; 0] B[0; 0] C[4.48221428571; 13.26331216314]
Centroid: CG[10.82773809524; 4.42110405438]
Coordinates of the circumscribed circle: U[14; 2.65877453619]
Coordinates of the inscribed circle: I[7.5; 5.38221363142]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.5798757281° = 150°34'44″ = 0.51334975555 rad
∠ B' = β' = 108.6722181629° = 108°40'20″ = 1.24549052788 rad
∠ C' = γ' = 100.749906109° = 100°44'57″ = 1.38331898193 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 = 27 ; ; c = 28 ; ;

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

p = a+b+c = 14+27+28 = 69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 69 }{ 2 } = 34.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34.5 * (34.5-14)(34.5-27)(34.5-28) } ; ; T = sqrt{ 34478.44 } = 185.68 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 185.68 }{ 14 } = 26.53 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 185.68 }{ 27 } = 13.75 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 185.68 }{ 28 } = 13.26 ; ;

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**2-27**2-28**2 }{ 2 * 27 * 28 } ) = 29° 25'16" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-14**2-28**2 }{ 2 * 14 * 28 } ) = 71° 19'40" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-14**2-27**2 }{ 2 * 27 * 14 } ) = 79° 15'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 185.68 }{ 34.5 } = 5.38 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 29° 25'16" } = 14.25 ; ;




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