What angle will make the resultant of three forces vertical? [with picture]

[SUCRALOSE]

I have tried everything on this one that I can think of.

I understand that the forces in the horizontal are 0, but I don't know where to start.

says: determine the angle for which the resultant of the three forces is vertical. See Picture.

 

[SUCRALOSE]

Please see this picture for above question.

 

[PeterO]

I have tried everything on this one that I can think of.

I understand that the forces in the horizontal are 0, but I don't know where to start.

says: determine the angle for which the resultant of the three forces is vertical. See Picture.

What is the sum of the horizontal components of the two, fully defined forces?

 

[SUCRALOSE]

The sum of the horizontal components, in the x direction, is:

70(cos140) + 80(cos165) = -131lb

to take it further;

70(sin140) + 80(sin165) = 66lb

r= (-131)2 + (66)2 = 147 lbs

inverse tan = 66/-131 = -27 degrees(I think I get it now) the resultant is vertical up.. so the sum of the left side is the same as right side...

 

[PeterO]

The sum of the horizontal components, in the x direction, is:

70(cos140) + 80(cos165) = -131lb

to take it further;

70(sin140) + 80(sin165) = 66lb

r= (-131)2 + (66)2 = 147 lbs

inverse tan = 66/-131 = -27 degrees


(I think I get it now) the resultant is vertical up.. so the sum of the left side is the same as right side...

Exactly, and with your creative use of 140^o and 165^o angles, you could simply have said

70(cos140^o) + 80(cos165^o) + 150(cosθ) = 0

 

[SUCRALOSE]

Thanks lots Peter,

At first I was trying to rearrange " 70(cos140o) + 80(cos165o) + 150(cosθ) = 0" for the unknown angle and was frustrated as to why that wouldn't work.

tricky trick question.

Thanks, now I can sleep, lol.