Sally is making a banner for her cousin's birthday party. She starts by cutting out triangle pieces of card stock paper; to not waste paper, she cuts the paper diagonally. Each piece of card stock 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 approximate angle formed at the base of the triangle, we need to use the properties of a right triangle since the paper was cut diagonally.
The height of the paper is given as 5 inches and the base is given as 3.5 inches.
Using the Pythagorean theorem, we can find the length of the hypotenuse:
hypotenuse^2 = height^2 + base^2
hypotenuse^2 = 5^2 + 3.5^2
hypotenuse^2 = 25 + 12.25
hypotenuse^2 = 37.25
hypotenuse ≈ √37.25
hypotenuse ≈ 6.102
To find the angle at the base, we can use inverse trigonometric functions. Since the base is adjacent to the angle and the hypotenuse is the longest side (opposite to the right angle), we can use the cosine function:
cos(angle) = base/hypotenuse
cos(angle) = 3.5/6.102
angle ≈ cos^(-1)(3.5/6.102)
angle ≈ 56.576 degrees
Therefore, the approximate angle formed at the base of the triangle is about 56.576 degrees.