The angle between the diagonal of a cube and an edge is
A) 45.0°.
B) 54.7°.
C) 90.0°.
D) 35.3°.

Question

Quizplus · Accepted Answer

The angle between the diagonal of a cube and an edge can be found using the dot product formula. For a cube with side length $a$, the diagonal's length is $a\sqrt{3}$ (using the Pythagorean theorem in three dimensions). The angle $\theta$ between the diagonal and an edge satisfies $\cos(\theta) = \frac{a}{a\sqrt{3}} = \frac{1}{\sqrt{3}}$, which gives $\theta \approx 54.7^\circ$.

The Angle Between the Diagonal of a Cube and an Edge