Question: I don't understand the DCL in k , why is the horizontal rope tension not used, what is the final result for displacement of k

I don't understand the DCL in k, why is the horizontal rope tension not used, what is the final result for displacement of k. How do I get the length of the bars. why only used vertical component. por favor podrias resolver esto en papel, no entiendo la solucion de la pagina.
I don't understand the DCL in k , why is the

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