We don't even really need trig... the cosine value is already shown in the diagram.
\(\Delta PQR \sim \Delta TSR\) because of AAA Similarity ... Angle STR is congruent to itself and angles PQR and TSR are both 90 degrees.
\(\frac{PQ}{TS}=\frac{5}{3}\), so this is the ratio for all sides.
Therefore, \(15 \div \frac{5}{3}=15 \times \frac{3}{5}=9\)
You are very welcome!
:P
