Answer:
![m\angle Z\approx22.0\textdegree](https://img.qammunity.org/2021/formulas/mathematics/high-school/qxfe7nzrmtjll05ijnhye33bny449mc2nv.png)
Explanation:
First, note that we have a right triangle. Second, we need to find angle Z, and we are given the sides opposite to angle Z and the hypotenuse. Therefore, we can use sine.
Recall that:
![\sin(\theta)=opp/hyp](https://img.qammunity.org/2021/formulas/mathematics/high-school/pa1d71pdv3u51ts0d9vpghxek926klzohr.png)
The opposite side is 3 while the hypotenuse is 8. Plug in the numbers and simplify. Use a calculator:
![\sin(\angle Z)=3/8\\\angle Z=\arcsin(3/8)\\\angle Z\approx 22.0243\textdegree](https://img.qammunity.org/2021/formulas/mathematics/high-school/37bkvdvlbw7cipaymrcp2u6uj9g32py19q.png)