Textbook Question
In Exercises 54–57, solve the right triangle shown in the figure. Round lengths to two decimal places and express angles to the nearest tenth of a degree. A = 22.3°, c = 10
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2. Trigonometric Functions on Right Triangles
Solving Right Triangles
1:00 minutesProblem 10
Textbook Question
Concept Check Refer to the discussion of accuracy and significant digits in this section to answer the following. WNBA Scorer Women's National Basketball Association player Breanna Stewart of the Seattle Storm was the WNBA's top scorer for the 2018 regular season, with 742 points. Is it appropriate to consider this number between 741.5 and 742.5? Why or why not? (Data from www.wnba.com)
Verified step by step guidance1
Understand the concept of significant digits and accuracy: When a number is reported as 742 points, it implies a certain level of precision, typically meaning the value is accurate to the nearest whole number.
Consider the meaning of the range 741.5 to 742.5: This range represents all values that would round to 742 when rounded to the nearest whole number.
Determine if the original number 742 can be considered within this range: Since 742 is rounded to the nearest whole number, it is appropriate to say the actual value lies somewhere between 741.5 and 742.5, assuming the data is rounded and not exact.
Reflect on the context of the data: In sports statistics, points are counted as whole numbers, so the value 742 is exact rather than an approximation, meaning it is not just an estimate within a range but a precise count.
Conclude whether it is appropriate to consider 742 between 741.5 and 742.5: Because the points are exact counts, it is not appropriate to treat 742 as an approximate value within that range; it should be considered an exact integer.
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Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Significant Digits and Rounding
Significant digits represent the precision of a measured or reported number. When rounding to a certain number of significant digits, the value is approximated within a range, typically ±0.5 of the last digit. Understanding this helps determine if a number like 742 can be considered between 741.5 and 742.5.
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Measurement Accuracy and Precision
Accuracy refers to how close a reported number is to the true value, while precision indicates the consistency or exactness of the measurement. In sports statistics, reported totals are often exact counts, not estimates, affecting whether ranges around the number are meaningful.
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Context of Data Reporting
The nature of the data—whether it is a counted total or a measured estimate—affects interpretation. Since points scored are discrete counts, the number 742 is exact, making it inappropriate to consider it as a range between 741.5 and 742.5, which applies more to measured values.
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