Resultant of thirty vectors of a polygon

[sadaf2605]

Thirty vectors, each of magnitude 2N, are represented by the sides of a regular polygon taken in order. Determine their resultants.

equation, square of resultant, R² = R_x² + R_y²


interior angle of a polygon = (n-2)* 180°/n
= (30 - 2)* 180°/30
= 168°
components on X axis:
A_x1 = 20* cos 168°
A_x2 = 20* cos (168°+168°)
. . . .
A_x30 = 20* cos (168° * 30)

R_x = A_x1 + A_x2 + . . . +A_x30

components on Y axis:
A_y1 = 20* sin 168°
A_y2 = 20* sin (168°+168°)
. . . .
A_y30 = 20* sin (168° * 30)

R_y = A_y1 + A_y2 + . . . +A_y30

thn,
R² = R_x² + R_y²




i think we can solve this kind of problem this way, but this process is so lengthy so i am expecting some alternative easy and short way to solve such problems, anyone to help?

The Attempt at a Solution

 

[AC130Nav]

I'm not sure I understand the problem.

If you add any number of vectors head-to-tail, and the head of the last one meets the tail of the first one, then the sum is always zero.

 

[sadaf2605]

I'm not sure I understand the problem.

If you add any number of vectors head-to-tail, and the head of the last one meets the tail of the first one, then the sum is always zero.

Thanks a lot!