2 28 29 triangle

Obtuse scalene triangle.

Sides: a = 2   b = 28   c = 29

Area: T = 24.66765259005
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 3.48331495666° = 3°28'59″ = 0.06107924283 rad
Angle ∠ B = β = 58.27437045405° = 58°16'25″ = 1.01770680116 rad
Angle ∠ C = γ = 118.2433145893° = 118°14'35″ = 2.06437322137 rad

Height: ha = 24.66765259005
Height: hb = 1.76218947072
Height: hc = 1.70111397173

Median: ma = 28.48768390665
Median: mb = 15.05499169433
Median: mc = 13.55554417117

Inradius: r = 0.83661534204
Circumradius: R = 16.46595533898

Vertex coordinates: A[29; 0] B[0; 0] C[1.05217241379; 1.70111397173]
Centroid: CG[10.01772413793; 0.56770465724]
Coordinates of the circumscribed circle: U[14.5; -7.78988958005]
Coordinates of the inscribed circle: I[1.5; 0.83661534204]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 176.5176850433° = 176°31'1″ = 0.06107924283 rad
∠ B' = β' = 121.7266295459° = 121°43'35″ = 1.01770680116 rad
∠ C' = γ' = 61.75768541071° = 61°45'25″ = 2.06437322137 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 = 2 ; ; b = 28 ; ; c = 29 ; ;

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

p = a+b+c = 2+28+29 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-2)(29.5-28)(29.5-29) } ; ; T = sqrt{ 608.44 } = 24.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 24.67 }{ 2 } = 24.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 24.67 }{ 28 } = 1.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 24.67 }{ 29 } = 1.7 ; ;

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{ 2**2-28**2-29**2 }{ 2 * 28 * 29 } ) = 3° 28'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-2**2-29**2 }{ 2 * 2 * 29 } ) = 58° 16'25" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-2**2-28**2 }{ 2 * 28 * 2 } ) = 118° 14'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 24.67 }{ 29.5 } = 0.84 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 3° 28'59" } = 16.46 ; ;




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