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Right triangles and trigonometry SAT question

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

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 $sin (J)$ ?

ExplanationShow

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 $\frac{308}{317}$ .

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 $sin (J)$ .

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Right triangles and trigonometry SAT question

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