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Because $\frac{b}{\sin\theta}$ is the length of the diagonal stretch of the rope.Why can $H = \left(\ell - \frac{b}{\sin\theta}\right)$ where $\ell$ is the length of the rope.
Due to all your help prior with tikz, I have been making pictures like this and better since last summer.Because $\frac{b}{\sin\theta}$ is the length of the diagonal stretch of the rope.
If you check out the math notes section and look at the pdfs I created, you will some more Latex pictures I created from what I learned from you.Glad to hear that. The picture looks nice!