Quick Resultant Forces Question

[Pablo1122]

Homework Statement

So we have 65N @ 30*, 30N @ 180* and 20N at 250*

Homework Equations

Ncos(angle)i + Nsin(angle)j

The Attempt at a Solution

Using this video



I did the following.

F1(65N) = 65cos(30)i+65sin30i

Then using the radian circle I saw that 30* has x,y coordinates of sqrt3/2 and 1/2 respectively. So as shown in the video I did

65(root3/2)i+65(1/2)j

= 56.3i + 32.5j

I did this for the left one too (30N).

But for the one at the bottom (20N) I get the degree of it to be 250. (270-20) = 250.

250* is not on the radian circle so how can I write 250* in terms of x,y coordinates?

If we look at this radian circle. We see that 240* = (-1/2, -sqrt3/2) and then it goes to 270* = (0,-1). How can I find the x,y coordinates for 250* and use it in the equation?

Thanks in advance.

 

[Doc Al]

How can I find the x,y coordinates for 250* and use it in the equation?

I don't believe that trig functions of that particular angle can be simply expressed. (Like the others can.) You'll need a calculator.

 

[Pablo1122]

I don't believe that trig functions of that particular angle can be simply expressed. (Like the others can.) You'll need a calculator.

Ah yes, I just found this out. Thanks!

 

[haruspex]

I don't believe that trig functions of that particular angle can be simply expressed. (Like the others can.) You'll need a calculator.

If it's a matter of expressing it in surds, you can use the usual expansion of sin(3x), with x=20^o, and apply the formula for solving cubics.