The figure at right 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.

The length of the crease is ...inches

To find the length of the crease, we can use trigonometry.

Let's label the length of the crease as "x".

Since the width of the strip is 12 inches, the distance from the crease to one of the edges is half of the width, which is 6 inches.

We can create a right triangle with the crease as the hypotenuse, and the adjacent side being 6 inches.

The angle between the hypotenuse and the adjacent side is 30 degrees.

Using trigonometry, we can use the cosine function to find the length of the crease:

cos(30 degrees) = adjacent / hypotenuse

cos(30 degrees) = 6 / x

To solve for x, we need to isolate it:

x = 6 / cos(30 degrees)

Using a calculator, we can find the value of cos(30 degrees) to be approximately 0.866.

x = 6 / 0.866

x ≈ 6.93 inches (rounded to two decimal places)

Therefore, the length of the crease is approximately 6.93 inches.

To find the length of the crease, we first need to understand the geometry of the folded paper.

Let's label the width of the strip as "w" (which is given as 12 inches) and the length of the crease as "l". Since the paper is folded in such a way that one corner meets the opposite edge, the crease creates a right triangle.

The angle formed by the crease (shown in the figure) is 30 degrees. The side opposite the 30-degree angle is the length of the crease, and the adjacent side is half of the width of the strip (since the strip is folded in half).

Using the trigonometric function tangent (tan), we can find the length of the crease. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side.

In this case, tan(30) = opposite/adjacent. We can substitute the values we know: tan(30) = l / (w/2).

Now, we can solve for the length of the crease (l):

l = tan(30) * (w/2)

Plugging in the values, we have:

l = tan(30) * (12/2)

Evaluating tan(30) to its decimal approximation, we have:

l ≈ 0.577 * 6

l ≈ 3.462 inches

Therefore, the length of the crease is approximately 3.462 inches.

No figure. Cannot copy and paste here.