Triangle FGH is similar to triangle JKL, 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 ) ?
Correct answer: B. 308/317
- A. 75/317
- B. 308/317
- C. 317/308
- D. 317/75
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 JKLand 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 measureof angle J, sin (F) = sin (J). It's given that sin (F) = 308/317. Therefore, sin(J) is 308/317.
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