28 29 30 triangle

Acute scalene triangle.

Sides: a = 28   b = 29   c = 30

Area: T = 363.2976624675
Perimeter: p = 87
Semiperimeter: s = 43.5

Angle ∠ A = α = 56.63329870308° = 56°37'59″ = 0.98884320889 rad
Angle ∠ B = β = 59.88217876035° = 59°52'54″ = 1.04551343557 rad
Angle ∠ C = γ = 63.48552253657° = 63°29'7″ = 1.1088026209 rad

Height: ha = 25.95497589053
Height: hb = 25.05549396327
Height: hc = 24.22197749783

Median: ma = 25.97111378264
Median: mb = 25.13546374551
Median: mc = 24.23883992871

Inradius: r = 8.35216465442
Circumradius: R = 16.76331615225

Vertex coordinates: A[30; 0] B[0; 0] C[14.05; 24.22197749783]
Centroid: CG[14.68333333333; 8.07332583261]
Coordinates of the circumscribed circle: U[15; 7.48435542511]
Coordinates of the inscribed circle: I[14.5; 8.35216465442]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 123.3677012969° = 123°22'1″ = 0.98884320889 rad
∠ B' = β' = 120.1188212397° = 120°7'6″ = 1.04551343557 rad
∠ C' = γ' = 116.5154774634° = 116°30'53″ = 1.1088026209 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 = 28 ; ; b = 29 ; ; c = 30 ; ;

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

p = a+b+c = 28+29+30 = 87 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 87 }{ 2 } = 43.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 43.5 * (43.5-28)(43.5-29)(43.5-30) } ; ; T = sqrt{ 131984.44 } = 363.3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 363.3 }{ 28 } = 25.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 363.3 }{ 29 } = 25.05 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 363.3 }{ 30 } = 24.22 ; ;

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{ 28**2-29**2-30**2 }{ 2 * 29 * 30 } ) = 56° 37'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-28**2-30**2 }{ 2 * 28 * 30 } ) = 59° 52'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-28**2-29**2 }{ 2 * 29 * 28 } ) = 63° 29'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 363.3 }{ 43.5 } = 8.35 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 28 }{ 2 * sin 56° 37'59" } = 16.76 ; ;




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