You are making a banner for your cousin's birthday party. You start by cutting out triangle pieces of cardstock paper; to not waste paper, you choose to cut the paper diagonally. Each piece of cardstock paper measures five inches in height with a base of three and a half inches. After cutting, what is the approximate angle formed at the base of the triangle? (1 point)

To find the angle formed at the base of the triangle after cutting the cardstock paper diagonally, we can use trigonometric relationships, specifically the tangent function.

Given:

• Height (opposite side) = 5 inches
• Base (adjacent side) = 3.5 inches

We can use the tangent function:

\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{5}{3.5} \]

Now, calculate the tangent value:

\[ \tan(\theta) = \frac{5}{3.5} \approx 1.4286 \]

Next, we need to find the angle \(\theta\) that corresponds to this tangent value by using the arctangent function:

\[ \theta = \tan^{-1}(1.4286) \]

Using a calculator to find this:

\[ \theta \approx 55° \]

Thus, the angle formed at the base of the triangle is approximately 55°.