Which saw is ideal for giving a smooth cut and is often used with a mitre box?

The back saw is designed with a stiffened spine and fine teeth, which allows it to produce very smooth and precise cuts, making it an ideal choice for detailed woodworking applications, such as those performed in a mitre box. The mitre box is a tool that helps to hold the workpiece at a specific angle for accurate cuts, and the back saw complements this setup well due to its ability to maintain control during the cutting process, resulting in clean edges necessary for projects like picture framing or cabinetry.

The other options, while useful for different purposes, do not provide the same level of precision. For instance, a crosscut saw is more suited for cutting wood across the grain but tends to produce a rougher edge. A keyhole saw is designed for making small cuts or curves in thin materials, and while versatile, it does not align with the need for smooth, straight cuts required in conjunction with a mitre box. Meanwhile, a hack saw is primarily used for cutting metal and has a different tooth configuration, which does not provide the smooth finish needed for woodworking projects. Thus, the features of the back saw make it the ideal choice for this specific task.