3 28 29 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 28   c = 29

Area: T = 40.2499223595
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 5.68994207757° = 5°41'22″ = 0.09992991251 rad
Angle ∠ B = β = 67.70990296252° = 67°42'33″ = 1.18217455003 rad
Angle ∠ C = γ = 106.6021549599° = 106°36'6″ = 1.86105480282 rad

Height: ha = 26.833281573
Height: hb = 2.87549445425
Height: hc = 2.77658085238

Median: ma = 28.4654890655
Median: mb = 15.13327459504
Median: mc = 13.6477344064

Inradius: r = 1.34216407865
Circumradius: R = 15.13107266477

Vertex coordinates: A[29; 0] B[0; 0] C[1.13879310345; 2.77658085238]
Centroid: CG[10.04659770115; 0.92552695079]
Coordinates of the circumscribed circle: U[14.5; -4.32330647565]
Coordinates of the inscribed circle: I[2; 1.34216407865]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 174.3110579224° = 174°18'38″ = 0.09992991251 rad
∠ B' = β' = 112.2910970375° = 112°17'27″ = 1.18217455003 rad
∠ C' = γ' = 73.3988450401° = 73°23'54″ = 1.86105480282 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 = 3 ; ; b = 28 ; ; c = 29 ; ;

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

p = a+b+c = 3+28+29 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-3)(30-28)(30-29) } ; ; T = sqrt{ 1620 } = 40.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 40.25 }{ 3 } = 26.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 40.25 }{ 28 } = 2.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 40.25 }{ 29 } = 2.78 ; ;

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{ 3**2-28**2-29**2 }{ 2 * 28 * 29 } ) = 5° 41'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-3**2-29**2 }{ 2 * 3 * 29 } ) = 67° 42'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-3**2-28**2 }{ 2 * 28 * 3 } ) = 106° 36'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 40.25 }{ 30 } = 1.34 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 5° 41'22" } = 15.13 ; ;




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