The figure below shows a long rectangular strip of
paper, one corner of which has been folded over to meet the opposite edge, thereby creating a 30-degree angle. Given that the width of the strip is 12 inches, find the length of the crease.
I labeled the side opposite to the $30^{\circ}$ angle as $x$ and the hypotenuse side would be $y$. The value for $x$ would be $y\sin(30) = x$. I also know that the hypotenuse of the smaller right triangle formed after the crease is also $x$ and the remaining width on the right would be $12-x$.
To solve for $y$, I thought of using the $\cos(60) = \frac{12-y\sin(30)}{y\sin(30)}$. The trouble is trying to find the value of $y$ from the cosine ratio of 60. I would appreciate it if someone can help me with that.
Thank you!
Best Answer
The length of the crease is 16 inches.