1. You could make an accurate diagram and measure R. This works but the computer won't like it. However you will know if you are correct. An answer ± 2 degrees would tell you that you are likely correct.
2. The second way is to find <C. Similarity guarantees that <C and <R are equal. The adjacent side to angle C is the second longest line. The second longest line in PQR is the adjacent side of <R.
Naturally we will use the second method, but you ought to try the first method. It's cumbersome but it will teach you how to read the values of triangles to make clear the trig functions.
and denote the sector area as 
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(the ratio between area is the same as the ratio between coresponding angles).
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