Question

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

Explanation:

Step1: Recall tangent formula

The tangent of an angle in a right - triangle is defined as $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$. For $\angle F$ in right - triangle $DEF$, the side opposite $\angle F$ 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:

$\frac{40}{9}$