Question

given right triangle def, what is the value of tan(f)?
9
41
40
40/41
40/9
41/9

Explanation:

Step1: Recall the tangent ratio formula

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

Step2: Identify the sides relative to angle \(F\)

For angle \(F\) in right - triangle \(DEF\), the side opposite to angle \(F\) is \(DE = 40\) and the side adjacent to angle \(F\) is \(DF=9\).

Step3: Calculate \(\tan(F)\)

Using the formula \(\tan(F)=\frac{\text{opposite}}{\text{adjacent}}\), we substitute the values: \(\tan(F)=\frac{DE}{DF}\). So, \(\tan(F)=\frac{40}{9}\)

Answer:

\(\frac{40}{9}\) (corresponds to the third option)