Triangle F G H is similar to triangle J K L , where angle F corresponds to angle J and

Question

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 = 308 317 , what is the value of sin ( J ) ?

Accepted Answer

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 = 308 317 . Therefore, sin J is 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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