Answer:
[tex]m\angle Z\approx22.0\textdegree[/tex]
Step-by-step 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:
[tex]\sin(\theta)=opp/hyp[/tex]
The opposite side is 3 while the hypotenuse is 8. Plug in the numbers and simplify. Use a calculator:
[tex]\sin(\angle Z)=3/8\\\angle Z=\arcsin(3/8)\\\angle Z\approx 22.0243\textdegree[/tex]
