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?
To find the angle at the base of the triangle, we can use the tangent of the angle.
tan(theta) = opposite/adjacent
In this case, the opposite side is 5 inches (height of the triangle) and the adjacent side is 3.5 inches (half the base of the triangle).
tan(theta) = 5/3.5
tan(theta) = 1.4286
Now, we can take the arctan to find the angle:
theta = arctan(1.4286)
theta ≈ 55.3 degrees
Therefore, the approximate angle formed at the base of the triangle is approximately 55.3 degrees.