We don't even really need trig... the cosine value is already shown in the diagram.
ΔPQR∼ΔTSR because of AAA Similarity ... Angle STR is congruent to itself and angles PQR and TSR are both 90 degrees.
PQTS=53, so this is the ratio for all sides.
Therefore, 15÷53=15×35=9
You are very welcome!
:P