Final answer:
To find the angle between a cube's diagonal and one of its edges, we use trigonometry. The angle can be found using the cosine function.
Step-by-step explanation:
To find the angle between a cube's diagonal and one of its edges, we can use trigonometry. Let's assume that the length of the cube's edge is 'a'. The diagonal of the cube can be found using the Pythagorean theorem: diagonal^2 = a^2 + a^2 + a^2. Simplifying this equation, we get diagonal = a * sqrt(3). The angle between the diagonal and the edge can be found using the cosine function: cos(angle) = adjacent/hypotenuse = a/(a * sqrt(3)) = 1/sqrt(3). Using a calculator, we find that the angle is approximately 54.7°, rounded to one decimal place.