Find Angles for Weight of 605 N

[jj8890]

[SOLVED] Force problem, need help

Homework Statement

Consider the 605 N weight held by two cables. The left-hand cable had tension 450 N and makes an angle of θ2 with the ceiling. The right-hand cable had tension 470 N and makes an angle of θ1 with the ceiling.
What are the angles θ1 and θ2 which are the angles of the right and left hand cables make with respect to the ceiling? Answer in units of degrees.

Homework Equations

sinθ=opp/hyp
cosθ=adj/hyp
sin^2θ + cos^2θ = 1

The Attempt at a Solution

I really do not know where to start here. I would appreciate any help. I am thinking that this has to do with using the above equations to find the angles but I am unsure how to use the 605 weight.

 

[Tedjn]

Before you break out the trigonometry, you should draw a diagram. Then, describe the motion (or lack of motion in this case) with some equations. Since this is a force problem, use F = ma. In these types of problems, break the forces on the weight into horizontal and vertical forces. Because the weight is motionless, the horizontal forces must sum to 0 and the vertical forces must sum to 0. What are providing the horizontal forces, and what are providing the vertical forces? How large are they?

Once you have your equations, you will find you have the sine or cosine of your angles θ₁ and θ₂ when you broke the forces from the cables into horizontal and vertical components. The rest is just solving for your angles.

 

[jj8890]

Ok, I understand that I would need to break the forces on the weight into horizontal and vertical but how exactly would you do that for the 450 N for example?

 

[Tedjn]

After you draw your diagram, draw a perpendicular line connecting the hanging weight to the ceiling from which the cables hang. This will break the triangle formed by your cables and the ceiling into two right triangles, from which you can use trigonometry to find the horizontal and vertical forces.