How Is the Angle Determined for the Opposite String in a Suspended Rod Scenario?

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In a suspended rod scenario, a uniform rod weighing 80 Newtons is in equilibrium at a 10-degree angle to the horizontal, with one string at a 40-degree angle to the vertical. To find the angle of the opposite string with the vertical, the equilibrium condition must be applied, ensuring that the sum of forces in both horizontal and vertical directions equals zero. By using geometric methods and analyzing the forces acting on the rod, the angle can be determined. The provided diagram aids in visualizing the forces and angles involved. The solution requires careful application of trigonometric principles to achieve the correct angle for the opposite string.
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A uniform rod of 80 Newtons is suspended from the ceiling by strings attached to its ends. The rod is in equilibrium at an angle of 10 degrees to the horizontal, and the string attached to the higher end is at an angle of 40 degrees tohe vertical. Find the angle which the other string makes with the vertical. (and please use the geometric method as this is the chapter i am learning now.) Thanks.
I have shown through diagram my working in the URL below. I just can't get the angle. Could you please get the angle for me.

http://farm6.staticflickr.com/5498/9993960885_c8d9523a07_b.jpg
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Just encase the link in -tags next time.
 
Use the fact that the rod is in equilibrium. The sum of forces is zero both in horizontal and vertical directions.
 

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