Question

If possible, find the length of EF. If not, explain why the length of EF cannot be determined

Answer 1

9514 1404 393

Answer:

  a.  yes; AA similarity

  b.  maybe 8, (or 30)

Step-by-step explanation:

a. The missing angle of ∆ABC is 180° -60° -20° = 100°. So, two of the angles of ∆ABC match those of ∆DEF, meaning the triangles are similar by the AA theorem.

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b. We notice the side ratios to be ...

  DE/AB = 12/9 = 4/3

Using that same ratio for corresponding sides ...

  EF/BC = 4/3

  EF = BC(4/3) = 6(4/3) = 8

Using the marked side lengths, we find EF = 8.

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We note that two angles and the side between them are sufficient information to solve ∆DEF with no reference to the markings of ∆ABC. Doing that, we find EF ≈ 30.4. We credit the discrepancy to the fact that ∆ABC is mis-marked. The longer side cannot be opposite the smaller angle.