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

Explanation:

Step1: Identify the trigonometric relation

In right - triangle $DEF$, $\tan\theta=\frac{opposite}{adjacent}$. Here, $\theta = 59^{\circ}$, the adjacent side to $\angle D$ is $DF = 3$, and the opposite side is $EF$. So, $\tan(59^{\circ})=\frac{EF}{3}$.

Step2: Solve for $EF$

We know that $\tan(59^{\circ})\approx1.6643$. Then $EF = 3\times\tan(59^{\circ})$. Substituting the value of $\tan(59^{\circ})$, we get $EF=3\times1.6643 = 4.9929$.

Step3: Round the answer

Rounding $4.9929$ to the nearest tenth gives $5.0$.

Answer:

$5.0$