find yz. write your answer as an integer or as a decimal rounded to the nearest tenth. yz =

Explanation:

Step1: Identify trig - function

In right - triangle $XYZ$ with right - angle at $Y$, we know $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 34^{\circ}$ and the hypotenuse $XZ=\sqrt{22}$, and we want to find the side $YZ$ which is adjacent to $\angle X$. So, $\cos X=\frac{YZ}{XZ}$.

Step2: Substitute values

We know that $\cos34^{\circ}\approx0.829$ and $XZ = \sqrt{22}\approx4.69$. Since $\cos X=\frac{YZ}{XZ}$, then $YZ = XZ\times\cos X$. Substituting the values, we get $YZ=\sqrt{22}\times\cos34^{\circ}$.

Step3: Calculate

$YZ\approx4.69\times0.829\approx3.9$.

Answer:

$3.9$