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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Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.
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