2023 AMC 12A Problems/Problem 15

Question

Usain is walking for exercise by zigzagging across a $100$ -meter by $30$ -meter rectangular field, beginning at point $A$ and ending on the segment $\overline{BC}$ . He wants to increase the distance walked by zigzagging as shown in the figure below $(APQRS)$ . What angle $\theta$ $\angle PAB=\angle QPC=\angle RQB=\cdots$ will produce in a length that is $120$ 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]

$\textbf{(A)}~\arccos\frac{5}{6}\qquad\textbf{(B)}~\arccos\frac{4}{5}\qquad\textbf{(C)}~\arccos\frac{3}{10}\qquad\textbf{(D)}~\arcsin\frac{4}{5}\qquad\textbf{(E)}~\arcsin\frac{5}{6}$

Solution 1

By "unfolding" line $APQRS$ into a straight line, we get a right angled triangle $ABS$ .

$cos(\theta)=\frac{120}{100}$

$\theta=\boxed{\textbf{(A) } cos^{-1}(\frac{5}{6})}$

Video Solution 1 by OmegaLearn

https://youtu.be/NhUI-BNCIUE

2023 AMC 12A (Problems • Answer Key • Resources)
Preceded by Problem 14	Followed by Problem 16
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All AMC 12 Problems and Solutions

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2023 AMC 12A Problems/Problem 15

Contents

Question

Solution 1

Video Solution 1 by OmegaLearn

See also