Answer:
5.0
Explanations:
From the given right triangle, we have the following side and angle:
[tex]\begin{gathered} XY=3(Adjacent) \\ m\angle X=59^0 \end{gathered}[/tex]
You are required to find the measure of YZ (Opposite side). To do that, you will apply the SOH CAH TOA trigonometry identity as shown:
[tex]\begin{gathered} \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \\ \tan m\angle X=\frac{YZ}{XY} \end{gathered}[/tex]
Substitute the given parameters into the resulting equation to get YZ:
[tex]\begin{gathered} \tan 59^0=\frac{YZ}{3} \\ YZ=3\tan 59^0 \\ YZ=3(1.6643) \\ YZ=4.9928 \\ YZ\approx5.0 \end{gathered}[/tex]
Therefore the measure of YZ to the nearest tenth is 5.0
