Triangle FGH is similar to triangle JKL, where angle F corresponds to angle J and angles G and K sin(F) = are right angles. If 308/317, what is the value of sin(J)?
Correct answer: B (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice B is correct. If two triangles are similar, then their corresponding angles are congruent. It’s given that right triangle FGH is similar to right triangle JKL 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 sin =sin sin = 308 equal to the measure of angle J, ^Fh ^Jh. It’s given that ^Fh 317. sin 308 Therefore, ^Jh is 317. cos sin Choice A is incorrect. This is the value of ^Jh, not the value of ^Jh. Choice C sin sin is incorrect. This is the reciprocal of the value of ^Jh, not the value of ^Jh. cos Choice D is incorrect. This is the reciprocal of the value of ^Jh, not the value of sin ^Jh. 43 SAT PRACTICE TEST #9 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 2
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