Question

Given right triangle DEF, what is the value of tan(F)?

Answer 1

Answer: $\frac{40}{9}$

Step-by-step explanation:

We know that for any angle x in a triangle ,

$\tan x=\frac{\text{side opposite to x}}{\text{side adjacent to x}}$

Now, for the given triangle DEF, the value of tan(F) is given by :-

$\tan F=\frac{\text{side opposite to F}}{\text{side adjacent to F}}\\\\\Rightarrow\ \tan F=\frac{40}{9}$

Hence, the value of tan(F) = $=\frac{40}{9}$

Answer 2

we know that

In the right triangle DEF

the tangent of the angle F is equal to

$tan(F)=\frac{opposite\ side\ angle\ F}{adjacent\ side\ angle\ F}=\frac{DE}{EF}$

substitute the values

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

therefore

the answer is the option

$\frac{40}{9}$