1. **State the problem:** We need to find the size of angle $HBG$ in a cuboid where $BH = 28$ cm and $BG = 21$ cm. 2. **Understand the geometry:** In a cuboid, edges meeting at a vertex are perpendicular. Points $B$, $H$, and $G$ form a right triangle with $B$ as the vertex where the angle is measured. 3. **Identify the triangle:** The angle $HBG$ is between edges $BH$ and $BG$ meeting at $B$. Since $BH$ and $BG$ are edges of the cuboid meeting at $B$, they are perpendicular. 4. **Calculate the angle:** Because $BH$ and $BG$ are perpendicular edges, the angle $HBG$ is $90^\circ$. 5. **Final answer:** The size of angle $HBG$ is $90.0^\circ$ to 3 significant figures.