Question

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

Explanation:

Step1: Recall the tangent formula

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For angle $F$, the opposite side is $DE = 40$ and the adjacent side is $DF=9$.

Step2: Calculate $\tan(F)$

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

Answer:

$\frac{40}{9}$