find ef.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\nef =

Answer:

$5.0$

Explanation:

Step1: Identify trigonometric relation

In right - triangle $DEF$, $\tan\theta=\frac{opposite}{adjacent}$. Here, $\theta = 50^{\circ}$, the opposite side to $\angle E$ is $DF = 6$, and the adjacent side is $EF$. So, $\tan E=\tan(50^{\circ})=\frac{DF}{EF}$.

Step2: Solve for $EF$

We know that $\tan(50^{\circ})\approx1.1918$ and $\tan(50^{\circ})=\frac{6}{EF}$. Then, $EF=\frac{6}{\tan(50^{\circ})}$. Substituting the value of $\tan(50^{\circ})$, we get $EF=\frac{6}{1.1918}\approx5.0$.