A carpenter is laying out a common rafter for a 6:12 pitch roof. The bird's mouth cut will sit on a 38 mm x 89 mm (2x4 nominal) top plate. What is the approximate plumb cut depth for the bird's mouth?

Question: A carpenter is laying out a common rafter for a 6:12 pitch roof. The bird's mouth cut will sit on a 38 mm x 89 mm (2x4 nominal) top plate. What is the approximate plumb cut depth for the bird's mouth?

Answer options:

• 38 mm
• 51 mm ✅ 76 mm
• 89 mm

Correct answer: 76 mm

Explanation: For a 6:12 pitch, the plumb cut angle is 26.57 degrees (tan inverse of 6/12). The depth of the plumb cut for the bird's mouth should be around two-thirds to three-quarters of the top plate width for adequate bearing while maintaining rafter strength. For an 89 mm (3.5 in) plate, two-thirds is approximately 59 mm (2.33 in). Three-quarters would be around 66 mm (2.6 in). The closest practical option, providing sufficient bearing and strength for a 2x4 top plate, is 76 mm (3 inches), commonly used to allow good bearing without significantly weakening the rafter.