Verified Answer :

calculista

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

\(\frac{40}{9}\)

JeanaShupp

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) = \(=\frac{40}{9}\)

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