given right triangle def, what is the value of tan(f)?

Explanation:

Step1: Recall tangent formula

In a right - triangle, $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$. For angle $F$ in right - triangle $DEF$, the side opposite to angle $F$ is $DE$ and the side adjacent to angle $F$ is $DF$.

Step2: Identify side lengths

We are given that $DE = 40$ and $DF=9$.

Step3: Calculate $\tan(F)$

Using the tangent formula $\tan(F)=\frac{DE}{DF}$. Substituting the values of $DE = 40$ and $DF = 9$, we get $\tan(F)=\frac{40}{9}$.

Answer:

C. $\frac{40}{9}$