2 29 30 triangle

Obtuse scalene triangle.

Sides: a = 2   b = 29   c = 30

Area: T = 25.53330667958
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 3.36550076185° = 3°21'54″ = 0.05987304623 rad
Angle ∠ B = β = 58.33217567465° = 58°19'54″ = 1.01880812137 rad
Angle ∠ C = γ = 118.3033235635° = 118°18'12″ = 2.06547809776 rad

Height: ha = 25.53330667958
Height: hb = 1.76109011583
Height: hc = 1.70222044531

Median: ma = 29.48772853956
Median: mb = 15.54883118055
Median: mc = 14.05334693226

Inradius: r = 0.8377149731
Circumradius: R = 17.03767313679

Vertex coordinates: A[30; 0] B[0; 0] C[1.05; 1.70222044531]
Centroid: CG[10.35; 0.56774014844]
Coordinates of the circumscribed circle: U[15; -8.07877605624]
Coordinates of the inscribed circle: I[1.5; 0.8377149731]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 176.6354992381° = 176°38'6″ = 0.05987304623 rad
∠ B' = β' = 121.6688243254° = 121°40'6″ = 1.01880812137 rad
∠ C' = γ' = 61.6976764365° = 61°41'48″ = 2.06547809776 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 = 29 ; ; c = 30 ; ;

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

p = a+b+c = 2+29+30 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-2)(30.5-29)(30.5-30) } ; ; T = sqrt{ 651.94 } = 25.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 25.53 }{ 2 } = 25.53 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 25.53 }{ 29 } = 1.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 25.53 }{ 30 } = 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**2-29**2-30**2 }{ 2 * 29 * 30 } ) = 3° 21'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-2**2-30**2 }{ 2 * 2 * 30 } ) = 58° 19'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-2**2-29**2 }{ 2 * 29 * 2 } ) = 118° 18'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 25.53 }{ 30.5 } = 0.84 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 3° 21'54" } = 17.04 ; ;




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