In right triangle R S T , the sum of the measures of angle R and

Choice B is correct. The sine of any acute angle is equal to the cosine of its complement. It’s given that in right triangle $RST$, the sum of the measures of angle $R$ and angle $S$ is $90$ degrees. Therefore, angle $R$ and angle $S$ are complementary, and the value of $\sin R$ is equal to the value of $\cos S$. It's given that the value of $\sin R$ is $\frac{\sqrt{15}}{4}$, so the value of $\cos S$ is also $\frac{\sqrt{15}}{4}$.

Choice A is incorrect. This is the value of $\tan S$.

Choice C is incorrect. This is the value of $\frac{1}{\cos S}$.

Choice D is incorrect. This is the value of $\frac{1}{\tan S}$.