Question

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

• $\frac{9}{41}$
• $\frac{40}{41}$
• $\frac{40}{9}$
• $\frac{41}{9}$

Explanation:

Step1: Recall tangent - ratio formula

In a right - triangle, $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$ for an acute angle $\theta$. 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 opposite and adjacent sides

We are given that $DE = 40$ (opposite to $\angle F$) and $DF=9$ (adjacent to $\angle F$).

Step3: Calculate $\tan(F)$

Using the formula $\tan(F)=\frac{\text{opposite}}{\text{adjacent}}$, we have $\tan(F)=\frac{DE}{DF}=\frac{40}{9}$.

Answer:

$\frac{40}{9}$