Question

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)
• 55°
• 35°
• 65°
• 45°

Answer 1

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°**.