find m∠f. write your answer as an integer or as a decimal rounded to the nearest tenth. m∠f = °

Explanation:

Step1: Recall trigonometric ratio

We use the tangent - ratio in right - triangle $\triangle EFD$. $\tan F=\frac{opposite}{adjacent}$. In right - triangle $\triangle EFD$ with right - angle at $E$, the side opposite to $\angle F$ is $ED = 3$ and the side adjacent to $\angle F$ is $EF = 2$.

Step2: Calculate the tangent value

$\tan F=\frac{ED}{EF}=\frac{3}{2}=1.5$.

Step3: Find the angle

We know that if $\tan F = 1.5$, then $F=\arctan(1.5)$. Using a calculator, $F=\arctan(1.5)\approx56.3^{\circ}$.

Answer:

$56.3$