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
Answer:B
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
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 (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.