1. **State the problem:** We have a cuboid ABCDEFGH with given lengths AD = 9 cm, FD = 13 cm, and angle GHF = 49°. We need to find the size of angle FAH, rounded to the nearest degree. 2. **Understand the cuboid and points:** In a cuboid, edges meeting at a vertex are perpendicular. Points F, A, H, and D are vertices of the cuboid. We use the given angle GHF = 49° to find relationships between edges. 3. **Identify vectors:** Consider vectors $ \overrightarrow{FA} $ and $ \overrightarrow{AH} $ to find angle FAH. 4. **Use the given lengths:** AD = 9 cm (height), FD = 13 cm (length), and angle GHF = 49° (angle between edges at vertex H). 5. **Calculate the length FH using angle GHF:** Since GHF is the angle between edges GH and HF, and GH is parallel to AD (9 cm), HF is 13 cm, then by cosine law in triangle GHF: $$ FH = \sqrt{GH^2 + HF^2 - 2 \times GH \times HF \times \cos(49^\circ)} $$ $$ FH = \sqrt{9^2 + 13^2 - 2 \times 9 \times 13 \times \cos(49^\circ)} $$ Calculate: $$ FH = \sqrt{81 + 169 - 234 \times \cos(49^\circ)} $$ $$ FH = \sqrt{250 - 234 \times 0.6561} $$ $$ FH = \sqrt{250 - 153.56} = \sqrt{96.44} \approx 9.82 \text{ cm} $$ 6. **Find angle FAH:** Vectors $ \overrightarrow{FA} $ and $ \overrightarrow{AH} $ are perpendicular edges meeting at A. Using the dot product formula: $$ \cos(\angle FAH) = \frac{\overrightarrow{FA} \cdot \overrightarrow{AH}}{|FA||AH|} $$ Since FA and AH are edges of the cuboid, their lengths are FD = 13 cm and AD = 9 cm respectively, and they are perpendicular, so angle FAH is 90°. 7. **Final answer:** $$ \boxed{90^\circ} $$ Angle FAH is 90 degrees.