Geometry-20 points-answer asap

i have zero clue what im doing (obviously by the wrong answer) can anyone explain how to do this? ? |
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  tan(F) = z/(2y)

Step-by-step explanation:

Make use of the similarity relationship to find the side necessary to compute the tangent. Then make use of the tangent definition.*

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The two triangles are given as being similar. That means corresponding sides have the same ratios:

  EF/AC = ED/AB

  ED = AB·(EF/AC) = 4z(x/(8x)) = (4/8)z = z/2

The mnemonic SOH CAH TOA reminds you that the tangent relationship is ...

  Tan = Opposite/Adjacent

  tan(F) = ED/DF = (z/2)/y

  tan(F) = z/(2y)

* Actually, you need to do this in reverse order: first you need to determine if you have all the necessary information to answer the question. You don't.

You need to know the length of side ED in terms of z. You notice that the corresponding side in similar triangle ABC has its length marked as a function of z, so all you need to find ED is the scale factor between the two triangles.

Since both hypotenuses are marked in terms of x, the scale factor is easily found.