2. Solve $\triangle P Q R$ if $r=38 \mathrm{~m}, p=18 \mathrm{~m}$, and $\angle Q=43^{\circ}$.

Step 1 ：\(\triangle PQR\) is given with \(r=38\mathrm{~m}\), \(p=18\mathrm{~m}\), and \(\angle Q=43^\circ\)

Step 2 ：Use the Law of Sines: \(\frac{p}{\sin{Q}} = \frac{r}{\sin{R}}\)

Step 3 ：Plug in the given values: \(\frac{18}{\sin{43^\circ}} = \frac{38}{\sin{R}}\)

Step 4 ：Solve for \(\sin{R}\): \(\sin{R} = \frac{38 \sin{43^\circ}}{18}\)

Step 5 ：Calculate \(\sin{R}\): \(\sin{R} \approx 0.9785\)

Step 6 ：Find \(\angle R\) using the inverse sine function: \(\angle R = \sin^{-1}(0.9785)\)

Step 7 ：Calculate \(\angle R\): \(\angle R \approx 77.5^\circ\)

Step 8 ：Find \(\angle P\) using the angle sum of a triangle: \(\angle P = 180^\circ - \angle Q - \angle R\)

Step 9 ：Plug in the values of \(\angle Q\) and \(\angle R\): \(\angle P = 180^\circ - 43^\circ - 77.5^\circ\)

Step 10 ：Calculate \(\angle P\): \(\angle P \approx 59.5^\circ\)

Step 11 ：Use the Law of Sines again to find side \(q\): \(\frac{q}{\sin{P}} = \frac{p}{\sin{Q}}\)

Step 12 ：Plug in the values of \(p\), \(\sin{P}\), and \(\sin{Q}\): \(\frac{q}{\sin{59.5^\circ}} = \frac{18}{\sin{43^\circ}}\)

Step 13 ：Solve for \(q\): \(q = 18 \frac{\sin{59.5^\circ}}{\sin{43^\circ}}\)

Step 14 ：Calculate \(q\): \(q \approx 25.6\mathrm{~m}\)

Step 15 ：\(\boxed{\angle P \approx 59.5^\circ, \angle R \approx 77.5^\circ, q \approx 25.6\mathrm{~m}}\)