Multiple Choice 11. Determine side $q$ in triangle $P Q R$ in which $\angle Q=90^{\circ}, \angle R=36^{\circ}$ and $r=15.9$ $\mathrm{cm}$. $27.1 \mathrm{~cm}$ $19.7 \mathrm{~cm}$ $21.9 \mathrm{~cm}$ $12.9 \mathrm{~cm}$

Step 1 ：Given that \(\angle Q=90^{\circ}\), we know that triangle \(PQR\) is a right triangle. We also know that \(\angle R=36^{\circ}\) and \(r=15.9\) cm.

Step 2 ：We can use the sine rule to find the length of side \(q\). The sine rule states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

Step 3 ：In this case, we have: \(\frac{r}{\sin R} = \frac{q}{\sin Q}\)

Step 4 ：We can rearrange this equation to solve for \(q\): \(q = \frac{r \cdot \sin Q}{\sin R}\)

Step 5 ：We can substitute the given values into this equation to find the length of side \(q\).

Step 6 ：Substituting the given values, we get \(q = 27.05069570559487\)

Step 7 ：Final Answer: The length of side \(q\) in triangle \(PQR\) is approximately \(27.1\) cm. Therefore, the correct answer is \(\boxed{27.1 \mathrm{~cm}}\).