Final answer:
A taper gauge is the tool that can be used to measure tapers when the work is in the lathe.
Step-by-step explanation:
The tool that can be used to measure tapers when the work is in the lathe is a taper gauge. Taper gauges are specifically designed to measure the degree of taper in objects, such as cylinders or cones. They consist of a set of thin metal plates or blades that can be inserted into the taper and provide a measurement of the taper angle.