# SAT Math Multiple Choice Question 233: Answer and Explanation

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**Question: 233**

**8.**

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

**Explanation:**

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 (a^{2} + b^{2} = c^{2}) to solve for DF. 11.2^{2} = 7^{2} + DF^{2}. 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.