Question

given right triangle def, what is the value of tan(f)?
option 1: \\(\frac{9}{41}\\)
option 2: \\(\frac{40}{41}\\)
option 3: \\(\frac{40}{9}\\)
option 4: \\(\frac{41}{9}\\)

Explanation:

Step1: Recall tangent definition

For an acute angle in a right triangle, $\tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}}$

Step2: Identify sides for $\angle F$

Opposite side to $\angle F$: $DE = 40$; Adjacent side to $\angle F$: $FD = 9$

Step3: Calculate $\tan(F)$

$\tan(F) = \frac{\text{opposite}}{\text{adjacent}} = \frac{40}{9}$

Answer:

$\boldsymbol{\frac{40}{9}}$ (corresponding to the third option: $\frac{40}{9}$)