In ArcMap, how can a user project a layer without using a geoprocessing tool?

The correct method for projecting a layer in ArcMap without using a geoprocessing tool involves setting the coordinate system of the data frame and then exporting the data using the coordinate system of the data frame. This process allows the user to apply a different spatial reference to the layer being worked with.

Projecting data involves defining how the layers should align spatially—this is inherent to the data frame settings. By setting the coordinate system of the data frame, you are specifying how the data should be presented based on its geographic location. When you then choose to export the data, the data is reprojected to match the coordinate system set for the data frame. This results in the desired layer output being in the correct coordinates and forms part of the output dataset.

Importing feature classes from a feature dataset or a geodatabase might assist in organizing and managing datasets, but these methods do not directly facilitate the projection of layers. They address creation and management rather than altering the spatial reference of the existing data. Therefore, the correct answer emphasizes the importance of the data frame's coordinate system as a primary factor in projection within ArcMap.