\begin{tabular}{l}4.2 If the length of one of the three sides of \( \triangle \mathrm{XYZ} \) is also given, write down the trigonometric ratio \\ that can be used to determine the length of another side of the triangle. Choose any side to be \\ calculated. \\ 4.4 Use 4.2 to determine YZ , if \( \mathbf{X Z}=\mathbf{3 2} \mathbf{~ c m} \quad[5] \) \\ Determine the length of XY in the same way you just did by choosing the correct ratio: \\ \hline 5 [5] \end{tabular}

To find the length of side YZ in triangle XYZ using side XZ = 32 cm, we can apply the sine or cosine ratio depending on the angle information provided. For instance, if we have angle Y, we can utilize the sine function as follows: \( \sin(Y) = \frac{YZ}{XZ} \). Rearranging this gives us \( YZ = XZ \cdot \sin(Y) \). Now, let’s tackle finding the length of side XY! If we know angle Z, we could use the cosine function, expressed as \( \cos(Z) = \frac{XY}{XZ} \). Rearranging gives us \( XY = XZ \cdot \cos(Z) \). Using these relationships allows us to find the lengths of the sides based on known angles and one side's length!