Given the figure, we can deduce the following information:
1. The measure of angle T is 45°.
2. The leg TS is:
[tex]32\sqrt[]{3}[/tex]
To determine SU, we use the formula:
[tex]\sin (\theta)=\frac{opposite}{\text{hypotenuse}}[/tex]
The opposite and hypotenuse sides are shown in the figure below:
We plug in what we know:
[tex]\begin{gathered} \sin (\theta)=\frac{opposite}{\text{hypotenuse}} \\ \sin (45)=\frac{SU}{32\sqrt[]{3}} \\ \text{Simplify and rearrange} \\ SU=\sin (45)(32\sqrt[]{3}) \\ SU=16\sqrt[]{6} \end{gathered}[/tex]
Therefore, the answer is:
[tex]\begin{gathered} SU=16\sqrt[]{6} \\ \end{gathered}[/tex]
