A cube-shaped storeroom has edges of 4 metres…

Step 1. The vectors. $\vec u = (4, 4, 0)$ with $\lvert\vec u\rvert = 4\sqrt{2}$, and $\vec w = (4, 4, 4)$ with $\lvert\vec w\rvert = 4\sqrt{3}$.

Step 2. The dot product. $\vec u\cdot\vec w = 16 + 16 + 0 = 32$.

Step 3. The cosine. $\cos\theta = \dfrac{32}{4\sqrt{2} \times 4\sqrt{3}} = \dfrac{2}{\sqrt{6}} = \dfrac{\sqrt{6}}{3} \approx 0.82$.

Step 4. The angle. $\theta = \cos^{-1}\dfrac{\sqrt{6}}{3} \approx 35.26^\circ$.