Determine the angle u for equilibrium

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The rod supports a weight of 200 lb and is pinned at its
end A. If it is also subjected to a couple moment of
100 lb * ft, determine the angle u for equilibrium. The spring
has an unstretched length of 2 ft and a stiffness of k = 50 lb/ft.
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wheeler
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Is there another way to solve this problem? I've never seen that trig identity in my life

justinclarke
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heads up
bro your website links to 5.58 instead of 5.60 this question, check it, still appreciate your work

akselcavak