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Right triangles and trigonometry SAT question

Math · Geometry and Trigonometry · Medium · Answer it here, explanation included.

In right triangle $R S T$ , the sum of the measures of angle $R$ and angle $S$ is $90$ degrees. The value of $sin (R)$ is $\frac{15}{4}$ . What is the value of $cos (S)$ ?

ExplanationShow

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 $R S T$ , 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 $\frac{15}{4}$ , so the value of $cos S$ is also $\frac{15}{4}$ .

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 $\frac{1}{tan S}$ .

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Right triangles and trigonometry SAT question

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