SAT Mathematics Practice Test 4

The angles marked $\mathit{x}°$ and $\mathit{y}°$ are acute angles in a right triangle. Thus, they are complementary angles. By the complementary angle relationship between sine and cosine, it follows that $\mathit{s}\mathit{i}\mathit{n}\left(\mathit{x}°\right)=\mathit{c}\mathit{o}\mathit{s}\left(\mathit{y}°\right)$. Therefore, the cosine of $\mathit{y}°$ is .6. Either .6 or the equivalent fraction $\frac{3}{5}$ may be gridded as the correct answer.
Alternatively, since the sine of $\mathit{x}°$ is .6, the ratio of the side opposite the $\mathit{x}°$ angle to the hypotenuse is .6. The side opposite the $\mathit{x}°$ angle is the side adjacent to the $\mathit{y}°$ angle. Thus, the ratio of the side adjacent to the $\mathit{y}°$ angle to the hypotenuse, which is equal to the cosine of $\mathit{y}°$, is equal to .6.