OG详解-OG3 数学1 Q17

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 equal to the measure of angle J , sin(F)= sin(J). It’s given that sin(F)= 308317​​. Therefore, sin(J ) is308317.
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).