You are taking a multiple-choice test that has 8 questions. Each of the questions has 4 answer choices, with one correct answe
r per question. If you select one of these choices for each question and leave nothing blank, in how many ways can you answer the questions?
1 answer:
You might be interested in
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.
__
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.
__
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.
