Finding the length

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How to determine the length of PR? enter image description here

We can determine the angle QSP and the length $SR$ then what to do?

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Compute $|SR|$ by relating $\cos(45^\circ)$ to $|QR|=2$ and $|RS|$.

Notice that $|QS|=|SR|$ (why?) and then compute $|PS|$ by relating $\tan(20^\circ)$ to $|PS|$ and $|QS|$.