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## Homework Statement

Hint: sin^2 [tex]\Theta[/tex] + cos^2[tex]\Theta[/tex] = 1 .

Consider the 600 N weight held by two

cables shown below. The left-hand cable had

tension 440 N and makes an angle of [tex]\Theta[/tex]2 with

the ceiling. The right-hand cable had tension

480 N and makes an angle of [tex]\Theta[/tex]1 with the

ceiling. What is the angle [tex]\Theta[/tex]1 which the right-

hand cable makes with respect to the ceiling?

Answer in units of ◦.

## Homework Equations

[tex]\Sigma[/tex]Fx=0

[tex]\Sigma[/tex]Fy=0

## The Attempt at a Solution

So, I understand all of the concepts perfectly well in order to complete this problem. The net force in both the x and y direction must be 0 in order for the system to remain at rest. Thus:

T1sin[tex]\Theta[/tex]1+T2sin[tex]\Theta[/tex]2=mg

T1cos[tex]\Theta[/tex]1=T2cos[tex]\Theta[/tex]2

In these two equations there are two unknowns: the two [tex]\Theta[/tex]s. So, if I solve for one, I can find the other. However, the issue here is the algebra. I'm not sure how to solve when I have cosine nested in arcsine, and such. Usually, I would turn to my TI-89 Titanium to solve this but it freezes. So, how am I to proceed? Any help is appreciated.