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Geometry and Trigonometry / Right triangles and trigonometry Difficulty: Medium

Triangle $F G H$ is similar to triangle $J K L$ , where angle $F$ corresponds to angle $J$ and angles $G$ and $K$ are right angles. If $\sin (F) = \frac{308}{317}$ , what is the value of $\sin (J)$ ?

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Explanation

Choice B is correct. If two triangles are similar, then their corresponding angles are congruent. It's given that right triangle $F G H$ is similar to right triangle $J K L$ and angle $F$ corresponds to angle $J$ . It follows that angle $F$ is congruent to angle $J$ and, therefore, the measure of angle $F$ is equal to the measure of angle $J$ . The sine ratios of angles of equal measure are equal. Since the measure of angle $F$ is equal to the measure of angle $J$ , $\sin (F) = \sin (J)$ . It's given that $\sin (F) = \frac{308}{317}$ . Therefore, $\sin (J)$ is $StartFraction 308 Over 317 EndFraction$ .

Choice A is incorrect. This is the value of $\cos (J)$ , not the value of $\sin (J)$ .

Choice C is incorrect. This is the reciprocal of the value of $\sin (J)$ , not the value of $\sin (J)$ .

Choice D is incorrect. This is the reciprocal of the value of $\cos (J)$ , not the value of $\sin (J)$ .