# Finding the Length of a Crease Given the Angle of Crease and Width of Paper

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!

• What is the problem? $\cos 60°=\sin30°=1/2$. Solve the equation to find $y=16$. – Aretino Nov 11 '17 at 16:31

## 2 Answers

The length of the crease is 16 inches. Hint: (This space intentionally left blank.)