14 28 30 triangle

Acute scalene triangle.

Sides: a = 14   b = 28   c = 30

Area: T = 194.9776921711
Perimeter: p = 72
Semiperimeter: s = 36

Angle ∠ A = α = 27.66604498993° = 27°39'38″ = 0.48327659233 rad
Angle ∠ B = β = 68.19662520106° = 68°11'47″ = 1.19902491351 rad
Angle ∠ C = γ = 84.14332980901° = 84°8'36″ = 1.46985775952 rad

Height: ha = 27.85438459588
Height: hb = 13.92769229794
Height: hc = 12.99884614474

Median: ma = 28.16602556807
Median: mb = 18.76216630393
Median: mc = 16.27988205961

Inradius: r = 5.41660256031
Circumradius: R = 15.0798707645

Vertex coordinates: A[30; 0] B[0; 0] C[5.2; 12.99884614474]
Centroid: CG[11.73333333333; 4.33328204825]
Coordinates of the circumscribed circle: U[15; 1.53986436372]
Coordinates of the inscribed circle: I[8; 5.41660256031]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.3439550101° = 152°20'22″ = 0.48327659233 rad
∠ B' = β' = 111.8043747989° = 111°48'13″ = 1.19902491351 rad
∠ C' = γ' = 95.85767019099° = 95°51'24″ = 1.46985775952 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 = 28 ; ; c = 30 ; ;

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

p = a+b+c = 14+28+30 = 72 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 72 }{ 2 } = 36 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36 * (36-14)(36-28)(36-30) } ; ; T = sqrt{ 38016 } = 194.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 194.98 }{ 14 } = 27.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 194.98 }{ 28 } = 13.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 194.98 }{ 30 } = 13 ; ;

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**2-28**2-30**2 }{ 2 * 28 * 30 } ) = 27° 39'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-14**2-30**2 }{ 2 * 14 * 30 } ) = 68° 11'47" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-14**2-28**2 }{ 2 * 28 * 14 } ) = 84° 8'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 194.98 }{ 36 } = 5.42 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 27° 39'38" } = 15.08 ; ;




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