\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}

1. To calculate a side using an angle and the hypotenuse in a right‑angled triangle, we can use one of the basic trigonometric ratios. For example, if we wish to find the side opposite an acute angle (say, angle \(X\)) then we use the sine function. That is, \[ \sin X=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{YZ}{XZ}. \] 2. Given that \(XZ=32\) cm and assuming the triangle is right‑angled (with \(XZ\) as the hypotenuse), we can determine \(YZ\) by rearranging the sine ratio: \[ YZ = XZ \cdot \sin X = 32 \cdot \sin X. \] 3. To determine the length of \(XY\) (which is adjacent to angle \(X\)), we use the cosine function: \[ \cos X=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{XY}{XZ}. \] Thus, \[ XY= XZ \cdot \cos X = 32 \cdot \cos X. \]