Question

Hi, can you help me to solve this exercise, please!!!

Answer 1

5.0

Explanations:

From the given right triangle, we have the following side and angle:

`\begin{gathered} XY=3(Adjacent) \\ m\angle X=59^0 \end{gathered}`

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:

`\begin{gathered} \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \\ \tan m\angle X=(YZ)/(XY) \end{gathered}`

Substitute the given parameters into the resulting equation to get YZ:

`\begin{gathered} \tan 59^0=(YZ)/(3) \\ YZ=3\tan 59^0 \\ YZ=3(1.6643) \\ YZ=4.9928 \\ YZ\approx5.0 \end{gathered}`

Therefore the measure of YZ to the nearest tenth is 5.0