find xz. write your answer as an integer or as a decimal rounded to the nearest tenth. xz =
find xz. write your answer as an integer or as a decimal rounded to the nearest tenth. xz =
Answer
Explanation:
Step1: Identify trigonometric relation
In right - triangle $XYZ$ with $\angle Y = 68^{\circ}$ and $YZ = 2$, we use the tangent function. $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\tan Y=\frac{XZ}{YZ}$.
Step2: Substitute values
We know that $Y = 68^{\circ}$ and $YZ = 2$. So, $\tan68^{\circ}=\frac{XZ}{2}$. Since $\tan68^{\circ}\approx2.475$, then $XZ = 2\times\tan68^{\circ}$.
Step3: Calculate $XZ$
$XZ=2\times2.475 = 4.95\approx5.0$.
Answer:
$5.0$