Difference between revisions of "2023 AMC 12A Problems/Problem 15"
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Usain is walking for exercise by zigzagging across a <math>100</math>-meter by <math>30</math>-meter rectangular field, beginning at point <math>A</math> and ending on the segment <math>\overline{BC}</math>. He wants to increase the distance walked by zigzagging as shown in the figure below <math>(APQRS)</math>. What angle <math>\theta</math><math>\angle PAB=\angle QPC=\angle RQB=\cdots</math> will produce in a length that is <math>120</math> meters? (This figure is not drawn to scale. Do not assume that he zigzag path has exactly four segments as shown; there could be more or fewer.) | Usain is walking for exercise by zigzagging across a <math>100</math>-meter by <math>30</math>-meter rectangular field, beginning at point <math>A</math> and ending on the segment <math>\overline{BC}</math>. He wants to increase the distance walked by zigzagging as shown in the figure below <math>(APQRS)</math>. What angle <math>\theta</math><math>\angle PAB=\angle QPC=\angle RQB=\cdots</math> will produce in a length that is <math>120</math> meters? (This figure is not drawn to scale. Do not assume that he zigzag path has exactly four segments as shown; there could be more or fewer.) | ||
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<math>\textbf{(A)}~\arccos\frac{5}{6}\qquad\textbf{(B)}~\arccos\frac{4}{5}\qquad\textbf{(C)}~\arccos\frac{3}{10}\qquad\textbf{(D)}~\arcsin\frac{4}{5}\qquad\textbf{(E)}~\arcsin\frac{5}{6}</math> | <math>\textbf{(A)}~\arccos\frac{5}{6}\qquad\textbf{(B)}~\arccos\frac{4}{5}\qquad\textbf{(C)}~\arccos\frac{3}{10}\qquad\textbf{(D)}~\arcsin\frac{4}{5}\qquad\textbf{(E)}~\arcsin\frac{5}{6}</math> | ||
Revision as of 23:55, 9 November 2023
Question
Usain is walking for exercise by zigzagging across a 
-meter by 
-meter rectangular field, beginning at point 
and ending on the segment 
. He wants to increase the distance walked by zigzagging as shown in the figure below 
. What angle 
will produce in a length that is 
meters? (This figure is not drawn to scale. Do not assume that he zigzag path has exactly four segments as shown; there could be more or fewer.)
[someone add diagram]
Solution 1
By "unfolding" line 
into a straight line, we get a right angled triangle 
.
Video Solution 1 by OmegaLearn
See also
| 2023 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 14 |
Followed by Problem 16 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
