SAT Math Multiple Choice Question 233: Answer and Explanation

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Question: 233


In the figure above, if sin a = cos b, which of the following is closest to the length of DF ?

  • A. 5.6
  • B. 8.7
  • C. 11.2
  • D. 12

Correct Answer: B


B Remember that sin a = cos b means that a and b are complementary angles. Therefore, the two triangles are similar and cos a = sin b as well and you can set up the following equation: = Now that you have solved for EF (11.2), you can use the Pythagorean theorem (a2 + b2 = c2) to solve for DF. 11.22 = 72 + DF2. The correct answer is (B). Alternatively, you could have used the Pythagorean theorem to solve for BC and then set up a proportion between the similar triangles. Just make sure that you recognize that AC corresponds to DE rather than DF.

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