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Geometry and Trigonometry / Right triangles and trigonometry Difficulty: Medium

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 $StartFraction StartRoot 15 EndRoot Over 4 EndFraction$ . What is the value of $\cos (S)$ ?

$StartFraction StartRoot 15 EndRoot Over 15 EndFraction$

$StartFraction StartRoot 15 EndRoot Over 4 EndFraction$

$StartFraction 4 StartRoot 15 EndRoot Over 15 EndFraction$

$StartRoot 15 EndRoot$

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Explanation

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 $StartFraction StartRoot 15 EndRoot Over 4 EndFraction$ , so the value of $\cos S$ is also $StartFraction StartRoot 15 EndRoot Over 4 EndFraction$ .

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

Choice C is incorrect. This is the value of $StartFraction 1 Over cosine upper S EndFraction$ .

Choice D is incorrect. This is the value of $StartFraction 1 Over tangent upper S EndFraction$ .