How Do You Calculate the Angle Theta1 for Equilibrium in a Two-Cable System?

[wmrunner24]

Homework Statement

Hint: sin^2 $$\Theta$$ + cos^2$$\Theta$$ = 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 $$\Theta$$2 with
the ceiling. The right-hand cable had tension
480 N and makes an angle of $$\Theta$$1 with the
ceiling. What is the angle $$\Theta$$1 which the right-
hand cable makes with respect to the ceiling?
Answer in units of ◦.

Homework Equations

$$\Sigma$$Fx=0
$$\Sigma$$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$$\Theta$$1+T2sin$$\Theta$$2=mg
T1cos$$\Theta$$1=T2cos$$\Theta$$2

In these two equations there are two unknowns: the two $$\Theta$$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.

 

[rock.freak667]

For this equation

T₁cosθ₁=T₂cosθ₂

Try squaring both sides and then use the hint to get a new equation in terms of sine.

 

[wmrunner24]

Genius. Worked great. Thanks a bunch.